GeomGravX: 10 Years of Geometric Foundations of Gravity and eXtensions (in Tartu)

29 Jun 2026, 09:00 → 3 Jul 2026, 16:05 Europe/Tallinn

A106 (Physicum, University of Tartu)

Christian Pfeifer (University of Bremen, ZARM), Daniel Blixt, Laur Järv (University of Tartu), Margus Saal (University of Tartu), Maria Jose Guzman (University of Tartu, Estonia), Merce Guerrero (University of Aveiro), Sotirios Karamitsos (University of Tartu), Tomi Koivisto (University of Tartu)

The Tartu-based conference series Geometric Foundations of Gravity (GeomGrav), together with its biannual extensions Teleparallel Gravity (TeleGrav) and Metric-Affine Frameworks for Gravity (MafFGrav), celebrate their 10th anniversary in 2026.

GeomGravX, this year’s edition of the scientific meeting on gravity and fundamental physics in Tartu, will focus on the wide range of approaches to gravity that eXtend the standard formalism of general relativity beyond a massless metric field in pseudo-Riemannian geometry derived from the Einstein–Hilbert action. The program will cover topics ranging from foundational mathematical aspects to observational tests of the gravitational interaction, including applications in cosmology, gravitational waves, black holes, quantization, and much more.

Topics under discussion will include (but not be limited to):

• Extensions of general relativity (metric-affine gravity, Poincare gauge gravity, scalar/vector/tensor gravity, teleparallel gravity, massive gravity, bi-metric gravity, etc.);
• Phenomenology of extended gravity (black holes, ordinary/neutron/boson/grava stars, gravitational waves, cosmology, dark energy, dark matter, galaxies, early universe, etc.);
• Beyond Lorentzian geometry in classical and quantum gravity (doubly/deformed relativity, standard model extension, Hamilton geometry, Finsler geometry, etc).

Special topic: Gravity Theory Research in the Age of AI

While the use of machine learning in data analysis is already commonplace, and large language models have found many applications beyond translation and textual editing, the revolutionary impact of AI on fundamental physics research is yet to be seen. The topic of the potential of AI to enhance research is frequently brought up in discussion and elicits a wide spectrum of opinions and responses. Therefore, the Friday morning session will focus on a critical assessment of positive and negative experiences the conference participants have had in using AI/LLM tools, as well as to the ethical and practical issues that inevitably arise. Discussion topics will range from making use of AI tools in symbolic algebra coding and in computer-assisted proofs, to approaches that aim to enhance theoretical understanding and knowledge and generate novel theories and results.

Plenary speakers

The list of plenary speakers include:

• Will Barker (Prague)
• Ginevra Braga (Gran Sasso)
• Mariam Bouhmadi-López (Bilbao)
• Kristina Giesel (Erlangen)
• David Mota (Oslo)
• Aneta Wojnar (Wrocław)

Acknowledgements

This conference is supported by the Estonian Research Council through the Center of Excellence TK202 "Foundations of the Universe" and the grants PRG2608, PSG910, MOB3JD1233, as well as by the Institute of Physics, University of Tartu. 

 

Monday 29 June

Opening words

Mariam Bouhmadi-López: TBA: Modified Gravity or Dark Energy as the Drivers of the Late-Time Acceleration of the Universe?

1 Modified Gravity or Dark Energy as the Drivers of the Late-Time Acceleration of the Universe?

Understanding the origin of cosmic acceleration and the persistent H_0 and S_8 tensions remains a major challenge in cosmology. In this talk, I explore alternatives to the standard LambdaCDM model based on both modified gravity and dynamical dark energy. Within the teleparallel framework, I discuss f(Q) and f(T) theories, showing how non-metricity and torsion can lead to novel cosmological dynamics, including the resolution of cosmological singularities and partial alleviation of current observational tensions. I also present several dark energy scenarios, including sign-switching dark energy, axion-inspired quintessence, and 3-form fields, and assess their observational viability using recent cosmological datasets. While none of the models fully resolves all existing discrepancies, several provide a better fit to the data and significantly reduce the Hubble tension. These results highlight the potential of both modified gravity and dynamical dark energy as promising frameworks for understanding the late-time evolution of the Universe.

Speaker: Dr Mariam Bouhmadi-López (University of the Basque Country)

TartuBouhmadiLopez2026Version1.pdf

10:05 Coffee break/poster viewing

Aneta Wojnar: Wave Phenomena Across Scales as Tests of Gravity: The FuSe CA24101 Initiative

This presentation introduces the FuSe Action (CA24101) and its main scientific challenges to a broad audience working on the mathematical formulation of fundamental interactions. A central focus of the talk is the role of thermodynamics in understanding physical phenomena. In particular, the presentation highlights the need for a consistent formulation of thermodynamics in systems governed by long-range interactions, especially gravitation, where standard approaches face significant limitations. The presentation will also outline the importance of the FuSe Action in fostering collaboration across disciplines and engaging researchers working on the foundations of physical theories, with the aim of advancing both theoretical understanding and practical applications.

2 Wave Phenomena Across Scales as Tests of Gravity: The FuSe CA24101 Initiative

This presentation introduces the FuSe Action (CA24101) and its main scientific challenges to a broad audience working on the mathematical formulation of fundamental interactions. A central focus of the talk is the role of thermodynamics in understanding physical phenomena. In particular, the presentation highlights the need for a consistent formulation of thermodynamics in systems governed by long-range interactions, especially gravitation, where standard approaches face significant limitations. The presentation will also outline the importance of the FuSe Action in fostering collaboration across disciplines and engaging researchers working on the foundations of physical theories, with the aim of advancing both theoretical understanding and practical applications.

Speaker: Dr Aneta Wojnar (University of Wroclaw)

wojnar_GeomGrav_X2026.pdf

Konstantinos Dialektopoulos: Primordial Black Holes as cosmic expansion accelerators

In this seminar, I will present a novel mechanism for cosmic acceleration driven by primordial black holes with effective repulsive behavior. Using a new Swiss Cheese cosmological framework, I will discuss four black hole spacetimes—Hayward, Bardeen, Dymnikova, and de Sitter-Schwarzschild—to show that this acceleration emerges naturally from the geometry itself. The results suggest that ultra-light PBHs could drive inflation without requiring an inflaton, while PBHs with masses  and abundances , slightly before matter-radiation equality, can produce a substantial amount of early dark energy, helping to alleviate the Hubble tension.

3 Primordial Black Holes as cosmic expansion accelerators

In this seminar, I will present a novel mechanism for cosmic acceleration driven by primordial black holes with effective repulsive behavior. Using a new Swiss Cheese cosmological framework, I will discuss four black hole spacetimes—Hayward, Bardeen, Dymnikova, and de Sitter-Schwarzschild—to show that this acceleration emerges naturally from the geometry itself. The results suggest that ultra-light PBHs could drive inflation without requiring an inflaton, while PBHs with masses $m \sim 10^{12}\mathrm{g}$ and abundances $0.107 < \Omega^\mathrm{eq}_\mathrm{PBH}< 0.5$, slightly before matter-radiation equality, can produce a substantial amount of early dark energy, helping to alleviate the Hubble tension.

Speaker: Dr Konstantinos Dialektopoulos (University of Malta)

Tartu_talk.pdf

11:50 Lunch Break

Monday Parallel A1

4 Francesca Spinato: Canonical and non-canonical symmetries in f(R) cosmology

The f(R)-gravity represents the most straightforward extension of the General Relativity. Among the different possible formulations, the starting action can be selected using the Noether symmetry approach, a phisically motivated criterion based on Noether's theorem aimed at identifying viable models that exhibit symmetries. An advantage in applying such an approach is the reduction of the dynamical system and the associated minisuperspace, thus enabling the derivation of exact solutions to the equations of motion. In this study, we consider the f(R) gravity in a cosmological context and study the canonical and non canonical cases comparing the conserved quantities corresponding to symmetries in the selected models. For the non canonical case, we extend the Noether vector up to the second prolongation after finding out the transformation law for the second time derivative of fields that define our minisuperspace. The main goal is to understand if there are some differences both in the solutions of the Noether system and the corresponding conserved quantities comparing the two cases.

GeomGravX2026_290626_SPINNATO_FRANCESCA.pdf

5 Margarida Lima: Non–Minimally Coupled Weyl Connection Gravity: Cosmological Perturbations

In Non-Minimally Coupled Weyl Connection Gravity the spacetime geometry is not fully determined by the metric alone, but also involves the Weyl connection characterized by an independent non-metricity vector. As a result, the gravitational sector is enriched by a dynamical vector field, which contributes to the field equations and modifies the curvature terms. This model also introduces an additional force term, due to non-minimally coupling, that can mimic both dark matter and dark energy effects, while it still preserves Wey's original motivation to unify gravity and electromagnetism.

MLima.pdf

6 Mahmoud Hashim: Clustered unified dark sector cosmology

We consider unified dark sector models in which the fluid can collapse and cluster into halos, allowing for hierarchical structure formation to proceed as in standard cosmology. We show that both background evolution and linear perturbations tend toward those in Λ cold dark matter (ΛCDM) as the clustered fraction f→1. We confront such models with various observational datasets, with emphasis on the relatively well-motivated standard Chaplygin gas. We show that the strongest constraints come from secondary anisotropies in the cosmic microwave background (CMB) spectrum, which prefer models with f→1. However, as a larger Hubble constant is allowed for smaller f, values of f≃0.99 (rather than tending to exact unity) are favored when late universe expansion data is included, with f≃0.97 and H0≃70 km/s/Mpc allowed at the 2-σ level. Such values of f imply extremely efficient clustering into nonlinear structures. They may nevertheless be compatible with clustered fractions in warm dark matter based cosmologies, which have similar minimal halo mass scales as the models considered here. Tight CMB constraints on f also apply to the generalized Chaplygin gas, except for models that are already quite close to ΛCDM, in which case all values of 0≤f≤1 are allowed. In contrast to the CMB, large scale structure data, which were initially used to rule out unclustered unified dark matter models, are far less constraining. Indeed, late universe data, including the large scale galaxy distribution, prefer models that are far from ΛCDM. But these are in tension with the CMB data.

GeomGravX_26_mhashim_slides.pdf

GeomGravX_26_mhashim_slides.pptx

7 Orest Hrycyna: Two Structually unstable FLRW models and a new non-hyperbolic de Siter attractor

TBA

hrycyna_tartu_2026.pdf

Monday Parallel B1

8 Michal Stano: Static Spherically Symmetric Black Holes in regularised 4D Einstein-scalar-Gauss-Bonnet theory

We investigate static, spherically symmetric black holes in regularised four-dimensional Einstein–scalar–Gauss–Bonnet gravity, with the aim of determining whether the theory admits non-asymptotically flat solutions beyond the known special cases. Working in standard spherical coordinates, we use a Frobenius-type expansion of the symmetry-reduced field equations to classify possible local branches of the metric functions and scalar field. While the h=1 sector reproduces the known analytic family, the generic spherical gauge reveals a highly constrained but potentially viable candidate branch. We discuss the structure of this branch, its finite-order consistency checks, and the remaining problem of deriving the full coefficient recursion. Although preliminary, these results indicate a concrete semi-analytical route toward identifying (or ruling out) a more general static spherical black hole family within regularised 4DEsGB gravity.

stano.pdf

9 Peter Mészáros: Properties of generalized Schwarzschild spacetimes with extra dimensions

I will talk about static spacetimes that are spherically symmetric in three space dimensions, and have also n extra dimensions with Euclidean symmetry. I show that a specific ansatz leads to a limited set of vacuum solutions of the Einstein field equations, which can also be classified as Weyl solutions. I will talk about properties of these spacetimes investigated through the Kretschmann scalar, Newtonian mass defined through the Newtonian limit, Komar mass, Einstein, Landau--Lifshitz, and ADM mass. In addition to 1+3+n dimensional Minkowski spacetime, there are two classes of solutions. The first class is a trivial product of the Schwarzschild spacetime and Euclidean spaces in extra dimensions, while the second class is non-trivial. In the case with no horizon, there is a naked singularity, all masses are equal, and they are negative. In the case when there is a horizon, this horizon accommodates a physical singularity, which corresponds to Kaluza--Klein bubbles featuring exotic properties. Einstein, Landau--Lifshitz, and ADM masses are positive, while Newtonian and Komar masses are negative. This differentiates these solutions from trivial higher-dimensional extensions of the Schwarzschild solution.

Meszaros_Peter_EstoTartu.pdf

10 Mindaugas Karciauskas: Primordial Black Holes from Resonances in the Running-Mass-Inflation Model

Resonant excitations during inflation can amplify the primordial curvature perturbation within a narrow range of k values. This suggests a novel mechanism to generate Primordial Black Holes (PBHs). We study such resonances within the context of the Running-Mass-Inflation model. Generated PBHs can explain the totality of Dark Matter. The mechanism also predicts enhanced induced Gravitational Waves (GWs) and GWs created by binary BH collisions. They will be observable by future laser interferometers and resonant cavity experiments respectively.

GeomGravX-M.Karciauskas.pdf

11 Adel Awad: Thermodynamics and Phase Structure of Dyonic Taub-NUT-AdS Spaces

We investigate the phase structures of Lorentzian Dyonic Taub-NUT-AdS spacetimes with spherical, flat, and hyperbolic horizon geometries. First, we construct a consistent approach for the thermodynamics of these solution, which is verified through the first law, the Gibbs-Duhem relation, and the generalized Smarr relation. Second, to analyze these phases we consider both canonical and mixed ensembles. Our analysis of the phase structure, in the spherical case, shows some intriguing features. It shows the existence of two distinguished critical points with a region of continuous phase transitions in between, and the possibility of merging the two into one. Furthermore, the flat and hyperbolic cases behave differently, in comparison with Van der Waals fluids. In these cases, the continuous phase transition occurs at low temperatures and pressures i.e., below the critical point and in contrast with the Van der Waals behavior.

Dyonic-TN-Phases-GGX.pdf

15:10 Coffee break

Monday Parallel A2

12 Ilaria Andrei: Cosmology and Inflation with Torsion and Nonmetricity

Metric affine gravity (MAG) represents an extension of general relativity (GR) in which the metric and affine connection are independent geometrical variables. This leads to two, in addition to curvature, tensors describing the geometry of spacetime, torsion and nonmetricity. And a new tensor describing its matter content together with the stress energy tensor, the hypermomentum tensor. I will review the main features of metric affine gravity and show the corresponding modified Friedmann equations. And I will present how MAG changes the GR predictions in the study fo cosmology and of inflation.

Slides_Ilaria_Andrei.pdf

13 Daniel Račko: Evolution of superhorizon perturbations in early Universe with anisotropic solid remnant

In this talk, I will discuss how a small anisotropic “solid remnant” left over after inflation could affect the early Universe. This model is inspired by solid inflation and its generalizations, in which matter is described by a triplet of fields. In our model, the full internal global Euclidean symmetry of this triplet is broken, leading to anisotropic expansion of the Universe. Superhorizon scalar and vector perturbations grow, while the behavior of tensor perturbations remains the same as in the standard case of a Universe filled only with radiation. The obtained results improve the agreement between observational data and the theoretical predictions of solid inflation in the case of suppressed nonlinear effects.

Tartu_2026_Racko.pdf

14 Sotirios Karamitsos: Temperature and Diffusivity in Frame-Invariant Scalar-Tensor Gravity

Scalar-tensor theories of gravity are known to generically admit an effective imperfect fluid description, which leads to a natural interpretation of GR as a state of thermal equilibrium. In particular, it is possible to assign a temperature to nonminimally coupled fields, which increases as the theory deviates from GR. However, this temperature is conformally dependent, and can be arbitrarily tuned, threatening its interpretation as an intrinsic property of a scalar-tensor theory (as opposed to a representation-dependent property). To remedy this, we employ the frame-invariant formulation of scalar-tensor gravity, in which all quantities are manifestly independent of the choice of conformal frame. We then find that all scalar-tensor theories, not just minimal ones, feature an identically vanishing temperature. As a result, the deviation from GR is a diffusive (rather than thermodynamical) process, controlled by the frame-invariant chemical potential, and so GR emerges as the state of diffusive equilibrium in the class of scalar-tensor theories (minimal or nonminimal).

KARAMITSOS_TALK_GEOMGRAVX.pdf

15 Adrián Casado-Turrión: Dissipative Phenomena in Scalar-Tensor Inflation

Physical processes (including field interactions and cosmological evolution) might have different interpretations in different conformal frames. In this talk, we shall discuss how to consistently transform dissipative phenomena between distinct conformal-frame representations of scalar-tensor gravity, and explore the observable consequences thereof in warm inflation scenarios, where the inflaton field is allowed to interact with a near-equilibrium thermal bath.

Monday Parallel B2

16 Lucy Zheng: Space-time structure and phenomenology of Cartan Khronon theory

Cartan Khronon framework provides a foundation for unconventional space-time structure with a clock field, dubbed ‘khronon’, which spontaneously breaks the symmetry between space and time. This allows gravitational theory to have a Spin(4) gauge structure with a Euclidean background. This talk aims to clarify the motivation for the Euclidean background, the procedure of dimensional Wick rotation, and provide a summary of phenomenological implications including dark matter effect that emerges as a by-product of gravitation, as well as recent developments in cosmology with the effect of spin current.

GeomGravX.LZ.pdf

17 Stylianos Papadopoulos: Gravitational Instantons and Chiral Reduction in Spin(4) Gauge theory of space-time.

In this talk, the Spin(4) gauge formulation of spacetime with a Cartan khronon field is presented. As motivation, the relation between Euclidean and Lorentzian descriptions is recalled as a Wick-rotation prescription relating two dynamically equivalent descriptions of the same underlying field configurations, once a time direction is selected by the Cartan khronon. Within this setting, the Spin(4) theory provides a gauge-theoretic description of spacetime in which the coframe structure emerges from the covariant derivative of the khronon field.
The full theory involves both self-dual and anti-self-dual sectors of the Spin(4) connection. A symmetry-breaking pattern is then discussed, in which the distinction between time and space selects a preferred structure and is accompanied by a chiral reduction of the gauge sector. This transition can be viewed as a passage from a Palatini-like Spin(4) phase to a self-dual (Ashtekar-like) formulation, in which only the self-dual sector governs the gravitational dynamics and reproduces the standard general relativistic behavior.
Within this chiral phase, gravitational instantons provide natural test configurations, as their (anti-)self-dual nature confines them to a single sector of the Spin(4) decomposition, allowing one to probe whether this sector alone reproduces the gravitational dynamics. This perspective is illustrated through the example of the Eguchi–Hanson gravitational instanton, which is presented as a first explicit instanton solution in this framework.\

Gravitational Instantons in Spin(4)-Cartan-Khronon_Papadopoulos_Stylianos.pdf

18 Priidik Gallagher: A practical guide to unifying the Khronon

A review of the question how to put the Cartan Khronon into a gauge-gravity unified field theory is provided. The issues are several-fold, from conceptual to technical: suggestions for future developments are provided. The Cartan Khronon is quite special in its particular balance of self-dual Einstein-Cartan gravity constrained to waywiser form, thus producing ideal dust. However, supplying the Cartan radius vector constraint is generic, to the point of uncertain novelty — gauge-gravity models are plenty. Meanwhile, conceptual issues remain: what should the gauge-gravity unified phase even be like? How to model the Khronon — as a symmetry breaking object, field of time, or metric constituent? Which way to execute the symmetry breaking, and from what to where? It is argued the problem itself is in a subtle mixing of problems in different domains, alas with unsure guidance, observational and otherwise. One calculable way forward is to span all Lagrangian possibilities, and identify physical viability by sector. Another philosophical path is to heavily devise interpretation, to limit the permutations. Which to prefer?

Gallagher_geomgravx.pdf

19 Mehraveh Nikjoo: Emulator-Assisted Investigation of Left-Right Symmetric Higgs Inflation

This work investigates inflation in a left-right symmetric extension of Higgs inflation, formulated in a first-order gravitational framework. Specializing to a single-field inflationary trajectory, the model admits two physically distinct cases: real , associated with complex-conjugate non-minimal couplings, and purely imaginary , associated with real non-minimal couplings.
We explore the parameter space of this inflationary model by comparing theoretical predictions with observational constraints on the scalar spectral index, scalar amplitude, and tensor-to-scalar ratio. Because direct numerical evaluation is expensive, the investigation uses an emulator-assisted pipeline combining Mathematica-generated inflationary observables, machine-learning classifiers and regressors, active candidate generation, and MCMC sampling. In both cases, the models reproduce Planck-compatible scalar predictions, while the tensor-to-scalar ratio remains broadly distributed below current bounds. Thus, current data do not strongly distinguish the real and imaginary coupling sectors.
Finally, we consider the physics of reheating as a way to further constrain the model.

inflation_presentation_mehraveh_nikjoo.pdf

Reception

Tuesday 30 June

David Mota: Cosmological Probes of Gravity Beyond General Relativity

Several modifications to general relativity have been proposed to explain the nature of dark energy and the accelerated expansion of the Universe. In this talk, I will review the current status of modified theories of gravity, focusing on astrophysical probes in the nonlinear regime. I will begin by outlining the expected behavior of theories beyond General Relativity in various astrophysical systems and their cosmological signatures. With this foundation, I will present a range of observational tests, emphasizing the use of current and next-generation observations for testing gravity. Specifically, I will demonstrate how physical observables in the nonlinear regime of structure formation serve as promising probes for constraining theoretical models in the nonlinear dynamics of galaxies, clusters, and large-scale structure.

10:05 Coffee break/Poster viewing

Saeed Rastgoo: A GUP-inspired quantum black hole: the static and rotating cases, and their phenomenology

I present a new model of a black hole derived systematically from deforming the canonical algebra inspired by the generalized uncertainty principle (GUP). This model has two quantum parameters controlling the onset and strength of quantum gravity effects. I will discuss the geometry of both the static case and the rotating model derived using Newman-Janis algorithm. Furthermore, I show how a comparison of the shadow of the rotating model with parameters of Sgr A and M87 obtained by the Event Horizon Telescope sets a bound on the quantum parameters of the model.

20 A GUP-inspired quantum black hole: the static and rotating cases, and their phenomenology

I present a new model of a black hole derived systematically from deforming the canonical algebra inspired by the generalized uncertainty principle (GUP). This model has two quantum parameters controlling the onset and strength of quantum gravity effects. I will discuss the geometry of both the static case and the rotating model derived using Newman-Janis algorithm. Furthermore, I show how a comparison of the shadow of the rotating model with parameters of Sgr A and M87 obtained by the Event Horizon Telescope sets a bound on the quantum parameters of the model.

Speaker: Prof. Saeed Rastgoo (University of Alberta)

Manuel Hohmann: Gravity actions and symmetry breaking using Clifford algebras

Many different formulations of general relativity are known. The Palatini action, based on a Lorentz connection and tetrad, can be derived from the MacDowell-Mansouri action, which combines these variables into a Cartan connection. The latter is obtained via gauge fixing and thus explicit symmetry breaking of the Stelle-West action to retain only Lorentz symmetry; the latter enlarges the Lorentz gauge symmetry of the Palatini action to the de Sitter or anti de Sitter groups. A different formulation is the Plebanski action, which is obtained from the Palatini action by a decomposition of the complexified Lorentz algebra into its self-dual and anti-self-dual parts. In my talk I will show how the aforementioned reformulations of the Palatini action can be cast into a common form by lifting these actions to a spin bundle and embedding the Lorentz algebra into its corresponding Clifford algebra, which is further embedded into the de Sitter or anti de Sitter Clifford algebra. In particular, I will show how this leads to a novel formulation of the Plebanski action, which does not need complexification, and retains the larger symmetry of the Stelle-West action, as both can be obtained with the help of spontaneous symmetry breaking and self-dual / anti-self-dual split within the enlarged Clifford algebra instead. This new formulation invites for interesting generalizations, in particular non-minimally coupled spinor fields, scalar field couplings and symmetry breaking similar to the Higgs mechanism.

21 Gravity actions and symmetry breaking using Clifford algebras

Many different formulations of general relativity are known. The Palatini action, based on a Lorentz connection and tetrad, can be derived from the MacDowell-Mansouri action, which combines these variables into a Cartan connection. The latter is obtained via gauge fixing and thus explicit symmetry breaking of the Stelle-West action to retain only Lorentz symmetry; the latter enlarges the Lorentz gauge symmetry of the Palatini action to the de Sitter or anti de Sitter groups. A different formulation is the Plebanski action, which is obtained from the Palatini action by a decomposition of the complexified Lorentz algebra into its self-dual and anti-self-dual parts. In my talk I will show how the aforementioned reformulations of the Palatini action can be cast into a common form by lifting these actions to a spin bundle and embedding the Lorentz algebra into its corresponding Clifford algebra, which is further embedded into the de Sitter or anti de Sitter Clifford algebra. In particular, I will show how this leads to a novel formulation of the Plebanski action, which does not need complexification, and retains the larger symmetry of the Stelle-West action, as both can be obtained with the help of spontaneous symmetry breaking and self-dual / anti-self-dual split within the enlarged Clifford algebra instead. This new formulation invites for interesting generalizations, in particular non-minimally coupled spinor fields, scalar field couplings and symmetry breaking similar to the Higgs mechanism.

Speaker: Manuel Hohmann (University of Tartu)

Fernando Izaurieta: One Lagrangian to rule them all

A single geometric invariant fixes the relative normalization and structure of gravity, Yang-Mills theory, and fermion kinetic terms, including ghost freedom in the gravitational sector, without tuning. Our results establish a minimal geometric route to unification that does not rely on extra dimensions or symmetry breaking by hand. Unlike previous gauge-gravity constructions, the relative normalizations and ghost freedom emerge from a single Clifford-algebraic invariant, without explicit symmetry breaking.

22 One Lagrangian to rule them all

A single geometric invariant fixes the relative normalization and structure of gravity, Yang-Mills theory, and fermion kinetic terms, including ghost freedom in the gravitational sector, without tuning. Our results establish a minimal geometric route to unification that does not rely on extra dimensions or symmetry breaking by hand. Unlike previous gauge-gravity constructions, the relative normalizations and ghost freedom emerge from a single Clifford-algebraic invariant, without explicit symmetry breaking.

Speaker: Fernando Izaurieta (Universidad San Sebastián)

Group photo

11:55 Lunch break

Tuesday Parallel A1

23 Filippo Contino: Vacuum stability in Geometric Trinity of Gravity

The decay of a metastable (false) vacuum is a crucial non-perturbative phenomenon, as it plays an important role in constraining Standard Model and beyond the Standard Model physics. In particular, it has been shown that gravity can have a significant impact on the calculation of the decay rate. In this context, it is natural to ask whether different but classically equivalent formulations of gravity lead to the same physical predictions. In this talk, I will discuss vacuum decay in General Relativity and in its teleparallel and symmetric teleparallel formulations, namely TEGR and STEGR. Although these theories describe the same classical dynamics, it is of paramount importance to understand whether this equivalence persists also at the quantum level. In this respect, the analysis of vacuum stability may provide a particularly sensitive testing ground. The central question addressed in my talk is whether the decay rate of a false vacuum computed within TEGR or STEGR coincides with the corresponding result obtained in GR. I will show that the tunneling exponent remains unchanged, offering a non-trivial example in which the equivalence between different formulations of gravity extends beyond classical dynamics.

24 Sebastian Schuster: Geometric Foundations in and beyond Gravity—The Perspective of Particle Detector Models

Already in general relativity, much of the most interesting physics has to do with semi-classical extensions and their physical effects. Early on, foundational issues were addressed through the introduction of the Unruh–DeWitt detect model which allowed an operational notion of particle detection. This described the then-recently discovered, semi-classical effects—like the Unruh effect and Hawking evaporation—in terms of concrete, observable quantities. In this talk, I will present two ongoing projects on detector models beyond general relativity. The first example is taken from macroscopic electrodynamics: A detector moving in a uniaxial crystal will observe non-trivial detection rates even in inertial motion when moving at an angle to the optic axis. Geometrically, this example is a case of a bimetric theory (or more broadly, of a quartic dispersion relation). The second example is taken from analogue space-times, and demonstrates the non-trivial dependence on space-time dimension of a detector response: In odd space-time dimensions, the detector response will be bosonic/fermionic for fermionic/bosonic massless particles, while for massive particles the response is significantly more involved.

25 Jakob Palmkvist: The algebraic structure of gravity

It has been known since 1998 that the dynamics of the bosonic form fields in supergravity can be formulated as a twisted first-order self-duality relation in a Lie superalgebra. I will extend the formalism to the gravity sector and describe how Einstein's equations in vacuum can be derived in a similar way. Conversely, diffeomorphisms can be generalised and unified with gauge transformations for the form fields.

26 Armin van de Venn: Information Geometry from Divergences

We present information geometry from the perspective of divergences, which define a generally asymmetric notion of separation. From this starting point, we show how both the metric tensor and affine connection naturally emerge, and we emphasize the role of nonmetricity in this framework. Within this setting, we demonstrate that a Brownian bridge subject to a canonical physical constraint evolves exactly along an m-geodesic on the statistical manifold of Gaussian distributions. This provides an explicit example in which stochastic dynamics follows an informationally straight trajectory, in analogy with geodesic motion in general relativity. More broadly, our findings suggest that the asymmetry of divergence may carry genuine physical significance and may constitute a concrete step toward an equivalence principle for information.

Presentation.pdf

27 Tomi Koivisto: More on the physical foundations of geometry

The series of breakthroughs witnessed at the previous conferences erupted last summer into a full-scale revolution. Presently the foundations of physics and of all sciences are shaken by a kaleidoscopic turmoil. This is a moment at which to revisit the main theme of the conference series.
Physics cannot rest on a geometrical foundation. The fact that geometrical descriptions are available is "völlig nichtssagend" [Einstein]. Rather, we would interpret General Relativity as the "physicalisation of geometry" [Reichenbach], albeit this achievement was originally incomplete.
With the recent advent of the new paradigm, the realm of physics is dramatically expanding, superseding whole fields of inexact science. The geometrical picture that once consisted only of bare outlines is now filled in with colour, depth, texture -- life!

Tuesday Parallel B1

28 Sebastian Brezina: The teleparallel gravity and Noether's second theorem

It is well known that the Teleparallel Equivalent of General Relativity (TEGR) is locally dynamically equivalent to General Relativity in the absence of matter. However, for decades, discussions have persisted about this equivalence when matter is present. These discussions primarily focus on the choice of coupling prescription, whether to use the metric teleparallel or the Levi-Civita one, and the description of spinor fields.
In this talk, we address the situation with coupling prescriptions and spinor fields in TEGR. Using Noether's second theorem, we argue that the structure of Noether's identities in TEGR results in the Levi-Civita coupling. As a consequence, one can consistently describe spinor fields in TEGR. Moreover, Noether's identities also allow us to analyze the gauge structure of TEGR and the popular claim that TEGR can be viewed as a gauge theory of translations. We explain that the gauge symmetries in TEGR are diffeomorphisms and local Lorentz transformations, and that no (internal) translational gauge symmetry is present.

29 Carmen Ferrara: Primary constraints of newer general relativity

We study the primary constraint structure of newer general relativity, a gravity theory based on a torsionless teleparallel geometry. The gravitational action consists of a scalar built from quadratic combinations of the nonmetricity tensor with arbitrary coefficients in the Lagrangian. We perform a 3+1 decomposition of the Lagrangian and compute the canonical momenta associated with the metric. We characterize the primary constraints coming from the metric conjugate momenta by analyzing when the map between momenta and velocities becomes non-invertible, and organize the outcome through a fully nonlinear decomposition into scalar, vector and tensor sectors. We compare our results with others found in the literature.

30 Dario Sauro: 3+1 decomposition and Hamiltonian analyses in symmetric teleparallel theories

We perform a 3+1 decomposition in a general symmetric metric-affine theory, classifying the extrinsic tensors and deriving the generalized Gauss-Codazzi relations. The latter are exploited to perform the teleparallel limit in a model-independent fashion, thus identifying the extrinsic non-metricity tensor which plays the role of the extrinsic Riemannian curvature. We further prove that no other tensor field can induce new dynamical degrees of freedom. Moreover, by analyzing the Cauchy problem of STEGR we obtain constraints on the boundary terms and we conclude by building the Hamiltonian and performing the Hamiltonian analysis.

31 Lehel Csillag: On the inverse problem of calculus of variations for autoparallels

In metric–affine geometry, autoparallels are generically non-variational, i.e.\,, they are not the extremals of any action integral. The existence of a parametrization-invariant action principle for autoparallels is a long-standing open problem, which is equivalent to the so-called Finsler metrizability of the connection -- that is, to the fact that these autoparallels can be interpreted as Finsler geodesics.
In this talk, we address this problem for the class of torsion-free affine connections with vectorial nonmetricity, which includes, as notable subcases, Weyl and Schrödinger connections. For this class, we determine the necessary and sufficient conditions for the existence of a Finsler Lagrangian that metrizes the connection (and depends only algebraically on the metric and on the nonmetricity defining vector field). In the cases where such a Finsler Lagrangian exists, we construct it explicitly.

32 Joakim Flinckman: Gravity beyond a single metric: Ghost-free interactions of spin-2 fields

The fundamental interactions of nature are formulated in terms of fields classified by mass and spin. Two of the most successful theories, General Relativity (GR) and the Standard Model (SM), can be derived from fields of fixed mass and spin by imposing theoretical consistency conditions. The SM contains well-understood interactions for fields with spin s<2, whereas local interacting theories with s>2 face fundamental obstacles, placing s=2 in a special position. Spin-2 fields are intrinsically linked to gravity, yet theories of interacting spin-2 fields remain comparatively unexplored. Lovelock’s theorem essentially establishes GR as the unique theory for a single massless spin-2 field, so it is natural to ask whether GR is part of a larger structure, as electromagnetism was later understood to sit within electroweak theory. This may be relevant to open questions in gravitational physics, such as dark matter, dark energy, the Hubble tension, and, ultimately, quantum gravity. However, theories of interacting spin-2 fields are notoriously plagued by ghosts—pathological fields with negative kinetic energy—and requiring their absence severely restricts the allowed interactions. In this talk, I will discuss the idea of multi-gravity, focusing on theoretical consistency, ghost freedom and uniqueness results for interactions involving several spin-2 fields.

15:35 Coffee Break

Poster session

Short Excursion at Old Observatory

Public Lecture at Old Observatory: Ginevra Braga - From Questions to Discoveries: How AI Can Support Scientific Research

Ginevra Braga - From Questions to Discoveries: How AI Can Support Scientific Research

Wednesday 1 July

Will Barker: Next-generation model-building for torsion and non-metricity

33 Next-generation model-building for torsion and non-metricity

Particle dark matter, along with many ultraviolet scenarios, suggest
that additional low-energy degrees of freedom remain to be discovered.
Theories of new physics may be understood as data models, for which the
Lagrangian couplings are model parameters. The net worth of a theory is
determined by its Bayesian evidence: the likelihood of precision
cosmology data is multiplied by the prior probability of the couplings,
and integrated over the coupling-space. Precision cosmology has made
great advances both in the collection of data and the efficient
computation of likelihoods. But whilst the complementary programme of
manufacturing candidate models is very active, it is far less
systematic, and priors are seldom specified.

Taking metric-affine gravity as an example, we review the formal
requirements of perturbative model-building with torsion and
non-metricity fields. We then present a framework for massively
automating the construction of new physics models, designed to scale
with the ever-increasing volume of data. Numerical polology uses nested
sampling to identify unitary and technically natural regions in
metric-affine coupling-space. Such models form self-consistent effective
field theories, which is essential since the predictivity of a model
(the ability to compute a likelihood) is endowed by the systematics of
QFT alone. The framework is adapted to bosonic theories of the dark
sector: the phenomenological implications of arbitrary field content
(field number, rank and index-symmetry) can be systematically explored
with recourse to tools such as GetDist and Cobaya. The framework is
inspired by the SOFTSUSY/SARAH tools for supersymmetric model-building,
and builds directly on the PSALTer software for modified gravity. The
latter is computer algebra software, which scales badly with complexity:
numerical polology overcomes this technical hurdle and facilitates
data-driven model-building.

As an illustration, we derive simple posterior reweightings from black
hole superradiance, large scale structure, and gravitational wave
dispersion. We also discuss realistic prospects for more sophisticated
likelihood plugins. We then perform a high-resolution survey of the
coupling-space of symmetric rank-two fields, and rank-three fields
corresponding to torsion and non-metricity.

Speaker: Will Barker (Czech Academy of Sciences)

10:05 Coffee break

María-José Guzmán: Numerical relativity and hyperbolicity in teleparallel gravity

In this talk, I will present recent progress in the 3+1 formulation of the metric teleparallel and symmetric teleparallel equivalents of general relativity, TEGR and STEGR. For TEGR, I will discuss the linearized Hamilton's equations and their hyperbolicity properties. Although the original system of differential equations is not hyperbolic, we show that it can be recast as a strongly hyperbolic system through suitable variable redefinitions and the addition of constraints. For STEGR, I will examine how different treatments of boundary terms affect the Hamiltonian and Hamilton's equations. Specializing the theory to spherical symmetry, we find that the resulting evolution equations are only weakly hyperbolic. We stress the importance of strongly hyperbolic systems for numerical relativity applications, and discuss ongoing attempts towards numerical modeling. I will conclude by outlining how these results may extend to more general gravitational models, including general teleparallel gravity, scalar-torsion theories, scalar-nonmetricity theories, and related extensions.

34 Numerical relativity and hyperbolicity in teleparallel gravity

In this talk, I will present recent progress in the 3+1 formulation of the metric teleparallel and symmetric teleparallel equivalents of general relativity, TEGR and STEGR. For TEGR, I will discuss the linearized Hamilton's equations and their hyperbolicity properties. Although the original system of differential equations is not hyperbolic, we show that it can be recast as a strongly hyperbolic system through suitable variable redefinitions and the addition of constraints. For STEGR, I will examine how different treatments of boundary terms affect the Hamiltonian and Hamilton's equations. Specializing the theory to spherical symmetry, we find that the resulting evolution equations are only weakly hyperbolic. We stress the importance of strongly hyperbolic systems for numerical relativity applications, and discuss ongoing attempts towards numerical modeling. I will conclude by outlining how these results may extend to more general gravitational models, including general teleparallel gravity, scalar-torsion theories, scalar-nonmetricity theories, and related extensions.

Speaker: Maria Jose Guzman (University of Tartu, Estonia)

Martin Krššák: Teleparallel regularization of the gravitational action

Classical solutions with a finite action play an important role in the path integral quantization of gravity, black hole thermodynamics, and holography. While the teleparallel action avoids the need for boundary terms, it depends on a non-dynamical spin connection that effectively encodes the regularization. We study different choices of this spin connection, as well as various methods for evaluating the gravitational action. We show that consistent results require properly accounting for the role of singularities, and we examine the issue of uniqueness, which leads us to identify underlying symmetries of the teleparallel action.

35 Teleparallel regularization of the gravitational action

Classical solutions with a finite action play an important role in the path integral quantization of gravity, black hole thermodynamics, and holography. While the teleparallel action avoids the need for boundary terms, it depends on a non-dynamical spin connection that effectively encodes the regularization. We study different choices of this spin connection, as well as various methods for evaluating the gravitational action. We show that consistent results require properly accounting for the role of singularities, and we examine the issue of uniqueness, which leads us to identify underlying symmetries of the teleparallel action.

Speaker: Martin Krssak (Comenius University in Bratislava)

Christian Pfeifer: Unified field theories from cotangent bundle geometry: The Einstein Maxwell Equations

The unification of all physical fields into one mathematical object and the derivation of all physical field equations from that object in one framework is a long-lasting endeavor in fundamental physics. We suggest a new approach to achieve this goal by encoding physical fields into the geometry of the 1-particle phase space on spacetime (the cotangent bundle) through Hamilton geometry. The fundamental field, which contains information about all physical fields in spacetime and defines the phase space geometry, is a scalar field in phase space that is interpreted as a point-particle Hamiltonian. We construct an action principle for scalar fields in phase space and derive the corresponding scalar field equation. By choosing a specific scalar field, namely the Hamiltonian describing a charged particle in curved spacetime with an electromagnetic field, we show that this phase-space scalar field equation is equivalent to the coupled Einstein-Maxwell equations in spacetime, thus providing a geometric unification of gravity and electromagnetism. We further discuss how this approach differs from previous unification attempts and its potential for describing further physical fields and their dynamics in a unified manner in terms of phase-space geometry.

36 Unified field theories from cotangent bundle geometry: The Einstein Maxwell Equations

The unification of all physical fields into one mathematical object and the derivation of all physical field equations from that object in one framework is a long-lasting endeavor in fundamental physics. We suggest a new approach to achieve this goal by encoding physical fields into the geometry of the 1-particle phase space on spacetime (the cotangent bundle) through Hamilton geometry. The fundamental field, which contains information about all physical fields in spacetime and defines the phase space geometry, is a scalar field in phase space that is interpreted as a point-particle Hamiltonian. We construct an action principle for scalar fields in phase space and derive the corresponding scalar field equation. By choosing a specific scalar field, namely the Hamiltonian describing a charged particle in curved spacetime with an electromagnetic field, we show that this phase-space scalar field equation is equivalent to the coupled Einstein-Maxwell equations in spacetime, thus providing a geometric unification of gravity and electromagnetism. We further discuss how this approach differs from previous unification attempts and its potential for describing further physical fields and their dynamics in a unified manner in terms of phase-space geometry.

Speaker: Christian Pfeifer (University of Bremen, ZARM)

11:50 Lunch break

Conference Trip

Thursday 2 July

Kristina Giesel: TBA: Gravitationally induced decoherence: From theoretical models to applications in neutrino oscillations

37 Gravitationally induced decoherence: From theoretical models to applications in neutrino oscillations

In this talk some recent results in understanding gravitationally induced decoherence from the perspective of relational quantum gravity will be discussed. Starting from microscopic models in which matter fields are coupled to linearised gravity, a gauge-invariant formulation is constructed using relational observables defined in terms of geometric clocks in the context of a reduced phase space quantisation. In this framework, gravity is chosen as an environment for the matter system, leading to open system dynamics for the physical degrees of freedom in the matter sector. The dynamics of open quantum systems are described by quantum master equations. Recent relational open QFT models involving either a scalar or a photon field are presented. Particular consideration is given to the role of approximations such as the Markov and rotating wave approximations, as well as to the renormalisation of the master equation in the one-particle sector. Finally phenomenological implications are addressed, with a particular focus on applications in the context of neutrino oscillations. These results illustrate how microscopic, relationally defined models can both complement and constrain existing phenomenological decoherence models. Taken together, these results contribute to establishing a bridge between microscopic models inspired by quantum gravity and the phenomenological models commonly used to determine experimental bounds on decoherence parameters.

Speaker: Kristina Giesel

10:05 Coffee break/Poster viewing

Vojtech Pravda: Charged asymptotically flat and asymptotically (A)dS black holes in quadratic gravity

We study static, spherically symmetric, asymptotically flat and asymptotically (A)dS charged black holes in quadratic gravity. Using the conformal-to-Kundt method, we simplify the field equations and derive the solutions in the form of a power series with coefficients determined by a recurrent formula. In addition to charge and mass, these black holes possess one additional parameter – the Bach parameter, corresponding to the value of an invariant of the Bach tensor on the horizon. In the asymptotically flat case, this Bach parameter has to be fine-tuned in order to achieve asymptotic flatness. In contrast, for the asymptotically (A)dS case, there exist parameter regions (specifically for a sufficiently large cosmological constant) where this fine-tuning is not necessary, and the Bach parameter becomes a new, free parameter of the black hole.

38 Charged asymptotically flat and asymptotically (A)dS black holes in quadratic gravity

We study static, spherically symmetric, asymptotically flat and asymptotically (A)dS charged black holes in quadratic gravity. Using the conformal-to-Kundt method, we simplify the field equations and derive the solutions in the form of a power series with coefficients determined by a recurrent formula. In addition to charge and mass, these black holes possess one additional parameter – the Bach parameter, corresponding to the value of an invariant of the Bach tensor on the horizon. In the asymptotically flat case, this Bach parameter has to be fine-tuned in order to achieve asymptotic flatness. In contrast, for the asymptotically (A)dS case, there exist parameter regions (specifically for a sufficiently large cosmological constant) where this fine-tuning is not necessary, and the Bach parameter becomes a new, free parameter of the black hole.

Based on: Phys. Rev. D 110 (2024) 4, 044069, and Phys. Rev. D 113 (2026) 2, 024040

Speaker: Vojtech Pravda (Institute of Mathematics of the Czech Academy of Sciences)

Damianos Iosifidis: Lagrangian dynamics and Regge-like trajectories for microstructured test bodies

I will introduce the Lagrangian formulation of microstructured test bodies containing all spin, dilation and shear charges and moving in a generalized non-Riemannian background. Using the equations of motion derived by this formulation I will study the evolution of the dynamical rest mass of the body. I will show that, due to the presence of non-metricity, the dynamical rest mass is no longer not a constant of motion, even with the imposition of additional constraints. This leads to novel Regge-like trajectories involving the dilation and shear (i.e. hadronic) charges of the particle.

39 Lagrangian dynamics and Regge-like trajectories for microstructured test bodies

I will introduce the Lagrangian formulation of microstructured test bodies containing all spin, dilation and shear charges and moving in a generalized non-Riemannian background. Using the equations of motion derived by this formulation I will study the evolution of the dynamical rest mass of the body. I will show that, due to the presence of non-metricity, the dynamical rest mass is no longer not a constant of motion, even with the imposition of additional constraints. This leads to novel Regge-like trajectories involving the dilation and shear (i.e. hadronic) charges of the particle.

Speaker: Damianos Iosifidis

TartuTalkMotion2026 (1).pdf

TartuTalkMotion2026.pdf

Nassim Bozorgnia: Imprints of the Large Magellanic Cloud on the Milky Way dark matter halo

The Large Magellanic Cloud (LMC) induces a significant time-dependent gravitational perturbation on the Milky Way dark matter halo, altering the local phase-space distribution of dark matter in the Solar neighborhood. Cosmological simulations that sample potential Milky Way formation histories provide a powerful framework to characterize the dynamical response of the halo to such a massive satellite interaction. In this talk, I will discuss the imprint of the LMC-Milky Way system on the local dark matter distribution using state-of-the-art cosmological simulations. I will then discuss the consequences of these non-equilibrium features for dark matter phenomenology, including their impact on both standard and non-standard interaction models, spanning light and heavy dark matter scenarios.

40 Imprints of the Large Magellanic Cloud on the Milky Way dark matter halo

The Large Magellanic Cloud (LMC) induces a significant time-dependent gravitational perturbation on the Milky Way dark matter halo, altering the local phase-space distribution of dark matter in the Solar neighborhood. Cosmological simulations that sample potential Milky Way formation histories provide a powerful framework to characterize the dynamical response of the halo to such a massive satellite interaction. In this talk, I will discuss the imprint of the LMC-Milky Way system on the local dark matter distribution using state-of-the-art cosmological simulations. I will then discuss the consequences of these non-equilibrium features for dark matter phenomenology, including their impact on both standard and non-standard interaction models, spanning light and heavy dark matter scenarios.

Speaker: Nassim Bozorgnia

11:50 Lunch break

Thursday Parallel A

41 Diego Molina: Maxwellian gravity and the cosmological constant

Inspired by the power of algebraic expansions to reveal hidden structures in physical theories, we explore the role of infinite semigroup expansions in the context of gravitational theories, focusing on the derivation of Maxwellian gravity and its relation to the cosmological constant. By systematically extending the symmetry structure of AdS, we unveil a natural path leading from Poincaré symmetry to Maxwellian gravity, incorporating cosmological corrections in a controlled manner. This approach provides a structured framework to recover Maxwellian gravity as the subleading term in the expansion of AdS gravity in both 3 and 4 dimensions. Additionally, we discuss the implications of this formalism in the context of Chern-Simons gravity and its potential connection to post-Newtonian and post-Minkowskian corrections.

42 Justin Feng: Event horizon termination and the emergence of Lorentz signature

In this talk, I describe in detail how one might understand the termination of the event horizon of a black hole in terms of of quasiregular singularity characterized by points possessing two future-directed light cones and two past-directed light cones (in fact this spacetime is conformal to a region of the 1+1 trousers spacetime). I then discuss Euclidean signature shift-symmetric scalar-tensor theories from which one can extract a Lorentzian structure, and show how this theory can provide a microscopic description for the aforementioned singularities. I discuss some recent works on the emergence of Lorentzian dispersion relations and a model for the big bang, as well as some preliminary and ongoing work on understanding compact objects in this class of theories.

43 Philip Schwartz: Weyl-type theorems in Galilei and Carroll geometry

A classic theorem of Weyl (1921) states that a Weyl metric—a natural generalisation of a pseudo-Riemannian metric—is uniquely determined by its conformal and projective structures. This theorem forms the basis for the famous Ehlers–Pirani–Schild (EPS) axiomatic reconstruction (1972) of Lorentzian spacetime structure from light rays and the worldlines of massive particles.
An equivalent formulation of Weyl’s result is that a torsion-free linear connection compatible with a pseudo-Riemannian conformal structure is uniquely determined by its projective structure. We discuss analogous results for suitably defined notions of conformal structure for Galilei and Carroll geometry, i.e. for spacetime geometries arising as the Newtonian and ‘ultra-relativistic’ limits of Lorentzian geometry.

44 Pietro Isaia: A Variational Framework for Linearised Theories

The usual approach to perturbation theory presents some mathematical flaws. For instance, when studying gravitational waves (GW) around a Minkwoski background, one usually imposes the weak-field limit, requiring the spacetime metric to be the Minkowski metric plus a small perturbation. However, the bundle of Lorentzian metrics is neither linear nor affine; thus, the addition operation is not globally well-defined. Starting from this consideration, we analyse another approach to linearisation and perturbation theory, which is completely variational. This framework presents numerous advantages: it can be applied to any classical field theory (generality), it does not involve any approximation in the computations (exactness), and, most importantly, it allows to study linearisation around all solutions of the theory at the same time (globality). As a first example, we apply the framework to standard General Relativity and we show that linearised Einstein equations are a generalisation of GW equations around a general background, as expected. Finally, we present a few considerations on the existence of solutions and on conservation laws.

Thursday Parallel B

45 Miguel Zilhão: Exploring the Dynamics of Hairy Black Holes with Numerical Relativity

We report on the numerical evolutions of black holes with synchronized or resonant hair. We show that in the "very hairy" regime, the horizon gets naturally ejected from the center of its environment. This dynamical splitting is likely to be generic for sufficiently hairy BHs in the broader class of models with synchronized or resonant hair, but possible exceptions may exist.

46 João Luís: Oscillating images from dark matter scalar solitons

Real scalar fields, e.g. the axion, cannot condensate into stationary solitonic configurations to form starlike structures, eventually either dispersing or collapsing. However, by relaxing the stationarity condition on the metric, it has been shown that oscillatory solitonic solutions—known as oscillatons—exist. Oscillatons share several properties with boson stars, including comparable compactness and mass ranges. However, their time-dependent nature can lead to potentially discriminating observable signatures. In this work, we explore the observational properties of oscillatons. We find that stable oscillatory circular orbits exist, extending down to the center of the configuration, supporting the possibility of accretion disk structures within the star. We compute the deflection of light rays and verify that it is largely insensitive to the time dependence of the metric. Despite this, the oscillatory behavior of the redshift factor has a strong effect on the observed intensity profiles from accretion disks, producing a breathing-like image whose frequency depends on the mass of the scalar field. In fact, their oscillation period may lie within the observational windows of the Event Horizon Telescope for Sgr A∗ and M87∗, suggesting the possibility that this “twinkling" behavior could be tested via near-horizon imaging of these objects.

47 Hanna Liis Tamm: Polarimetric imprints of exotic compact objects

Recent observations of polarized light from galactic cores motivate the study of polarized exotic compact objects (ECOs), which can mimic the features of black holes (BHs) in the strong-field regime of gravity. In this work, the properties of three ultra-compact classes of models containing light rings are studied — relativistic thin-shell fluid spheres, thin-shell gravitational vacuum stars, and self-gravitating scalar boson stars coupled minimally to gravity via a solitonic potential. This work simulates the orbit of a hot spot around the considered ECOs in the ray-tracing software GYOTO, producing polarizational signatures and observables such as integrated images of the Stokes parameters , , ; their evolution during the orbit in the QU-plane, and the electric vector position angle (EVPA). Assuming a vertical magnetic field structure supported by observations by the GRAVITY and ALMA collaborations, the study focuses on qualitative differences between the models and in comparison with the BH scenario. One fluid star model mimicks the BH observables, while another gravastar produces notable differences in the EVPA curve. Regarding boson stars, the absence of a higher-order image causes one model to deviate from the expected signature of the -loop, eliminating it as a possible candidate. These results provide a useful tool to constrain the metric in current and future observations.

48 Ujjwal Agarwal: Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification

The complete set of covariant equations that govern the locally rotationally symmetric torsion spacetimes sourced by Weyssenhoff fluid in Einstein-Cartan-Sciama-Kibble gravity is presented. Using these equations, one can explore in detail the peculiar relationship between conformal structure and torsion. A comprehensive scheme to categorize these torsional spacetimes into distinct classes is developed. Further, the properties of each class are explicitly analyzed and novel analytical solutions to the gravitational field equations are obtained.

15:10 Coffee break

Panel discussion

Conference dinner

Friday 3 July

09:30 Morning coffee

Ginevra Braga: AI--Assisted Exploration: DHOST Theories without Quantum Ghosts: Ginevra Braga

Higher-derivative quantum corrections are essential ingredients of scalar-tensor effective field theories (EFTs), yet they generically reintroduce the Ostrogradsky ghost instability that the classical theory was designed to avoid. In this talk, we address this tension by establishing a rigorous equivalence between two independent criteria for theoretical consistency. We consider a general DHOST theory including its one-loop quantum corrections and derive consistency conditions through two complementary approaches. First, we obtain a system of differential equations by requiring invariance of the quantum-corrected action under the protective gauge symmetry of the classical theory. Second, we perform a Hamiltonian analysis in the ADM formalism, deriving the primary and secondary constraints necessary to eliminate the ghost degree of freedom. We then show that the resulting symmetry-based and dynamical consistency conditions are mathematically identical.
A distinctive feature of this work is the extensive use of a multi-agent AI system throughout the research process. Whereas AI is currently viewed primarily as a tool for relatively localized tasks such as coding or information retrieval, we investigate its potential role in the broader scientific workflow, including conjecture generation, exploration of theoretical structures, and the identification of nontrivial connections between independent formalisms. This work provides a first step toward assessing whether AI can contribute not only to technical execution but also to the investigation of fundamental questions in theoretical physics.

AI discussion

Closing words

13:00 Lunch break

14:30 Free discussion

Participants are free to use the conference venue for collaborations/discussions