Geometric Foundations of Gravity 2025

30 Jun 2025, 09:00 → 4 Jul 2025, 16:40 Europe/Tallinn

A106 (University of Tartu, Physicum)

Christian Pfeifer (University of Bremen, ZARM), Laur Järv (University of Tartu), Margus Saal, Sotirios Karamitsos (University of Tartu)

The conference is dedicated to the various approaches to gravity that venture beyond the basic formalism of general relativity, i.e., the description in terms of a massless metric field in Riemannian geometry derived from the Einstein-Hilbert action. The topics will range from the foundational issues to the applications in cosmology, gravitational waves, black holes, and other objects.

The topics under discussion include for instance:

• 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).

Workshop on computer algebra in gravity

The last day of the conference is planned for hands on tutorial workshops on using computer algebra in gravity theory calculations, focussing on free specialized software packages Cadabra and SymPy (tensor).

The plenary speakers include:

• Salvatore Capozziello (Napoli)
• Che-Yu Chen (Tokyo)
• Dražen Glavan (Prague)
• Kirill Krasnov (Nottingham)
• Antonino Marciano (Shanghai, Frascati)
• Nicoleta Voicu (Brasov)
• Thomas Złośnik (Gdansk)

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. The organisers are grateful to the University of Tartu Asia Centre for a travel grant supporting the visit of invited speaker Che-Yu Chen.

Monday 30 June

09:00 → 09:15 Opening Words

09:15 → 10:05 Cartan geometry and gravitation

It was discovered by the French mathematician Elie Cartan that the geometry of a surface could be revealed by rolling a ball on it. Remarkably, the mathematical description of this rolling process involve ingredients familiar from modern gauge theories. Cartan-geometrical descriptions of General Relativity and teleparallel gravity are presented and it is argued that typically Cartan-geometric descriptions of gravity will introduce new - and potentially phenomenologically relevant - degrees of freedom in the gravitational sector.

Speaker: Thomas Zlosnik (University of Gdansk)

PresentationPdf.pdf

10:05 → 10:35 Coffee Break

Coffee Break

10:35 → 11:25 Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality

We investigate a Schwarzschild metric exhibiting a signature
change across the event horizon, which gives rise to what we term a
Lorentzian-Euclidean black hole. The resulting geometry is regularized
by employing the Hadamard partie finie technique, which allows us to
prove that the metric represents a solution of vacuum Einstein
equations. In this framework, we introduce the concept of atemporality
as the dynamical mechanism responsible for the transition from a regime
with a real-valued time variable to a new one featuring an imaginary
time. We show that this mechanism prevents the occurrence of the
singularity and, by means of the regularized Kretschmann invariant, we
discuss in which terms atemporality can be considered as the
characteristic feature of this black hole. The physical foundation of
the approach can be related to the conservation laws. In fact, the black
hole is singularity free if Noether symmetries, related to the size and
the mass of the gravitational system, are not violated. In other words,
the emergence of imaginary time is the signature of a symmetry breaking.
In this perspective, it is not possible to enter the black hole, and the
event horizon becomes the limit of our knowledge according to the
standard laws of physics. Future challenges are related to the
observational signatures of atemporality which actually means that the
information comes only from the external black hole solution, and, in
addition, it is conserved. Other open issues are related to the quantum
counterpart of the model. In fact, we could conceive the event horizon
as a sort of potential barrier and the investigation of quantum
particles impacting against it could open an interesting phenomenology
to be explored.

Speaker: Salvatore Capozziello (INFN - National Institute for Nuclear Physics)

Capozziello_BH.pdf

11:25 → 11:50 Self-excited instantons and the non-trivial structure of the teleparallel vacuum

In this talk, I will review our new approach to constructing gravitational instantons in teleparallel gravity, based on the observation that the teleparallel action can be written as a product of torsion and excitation forms. This naturally leads to the idea of considering solutions in which these two forms are equal—solutions we call self-excited, in analogy with self-dual solutions in Yang-Mills theory. These self-excited solutions turn out to be instantons, with their action fully determined by the topological Nieh–Yan term, which leads to some insights about the topological aspects of teleparallel theories. We will present some of these results and provide possible evidence for the existence of a non-trivial vacuum structure, and discuss implications for our understanding of teleparallel gravity.

Speaker: Dr Martin Krssak (Comenius University in Bratislava)

Krssak_Presentation_2025_Tartu.pdf

11:50 → 13:30 Lunch

Lunch

13:30 → 15:05 Monday Parallel 1 - A106

13:30 Projective coordinate transformation in teleparallel cosmology

In the study of cosmology in teleparallel gravity, one can find a number of models whose dynamics turn out to have certain homogeneity properties, which allows finding a system of coordinates which separates the dynamics of "angular" and "radial" coordinates. In this split, one finds that the angular coordinates form a compact phase space, and that the qualitative dynamics in this part of the phase space (up to a positive factor, which can be absorbed in the time coordinate) are independent of the radial dynamics, and also determine the latter. As a consequence, phenomenological properties can be predicted from the angular dynamics alone. Further, it follows by compactness that a dynamical system approach always yields fixed points. In my talk I give some conditions for the existence of such coordinates and show how to apply this framework to a few example theories.

Speaker: Manuel Hohmann (University of Tartu)

13:55 Generalized Hidden Conformal Symmetry in Quadratic f(T) Gravity

We find the non-extremal charged rotating black holes in quadratic f (T ) gravity are holograph-
ically dual to two different hidden conformal field theories. The two conformal field theories can
be merged to find a very general hidden conformal field theory, which is generated by the SL(2, Z)
modular group. We also carry out the the calculation to the extremal limit of the black holes, and
find the corresponding dual quantities. Contrary to the existence of two different dual conformal
field theories for the extremal charged rotating black holes in Einstein gravity, we find only one
dual theory exists for the extremal charged rotating black holes in quadratic f (T ) gravity.

Speaker: Prof. Masoud Ghezelbash

BH.pdf

14:20 Kerr's spacetime energy in general teleparallel theory of relativity

The work addresses the calculation of the Kerr spacetime energy within the framework of the general teleparallel equivalent of general relativity. As an alternative to general relativity, teleparallel geometry is used instead of classical Riemannian geometry, where curvature is zero while torsion and non-metricity play an important role. Unlike the Schwarzschild metric, the Kerr metric allows for the description of the angular momentum of a central object. The work provides an overview of the geometric and physical foundations of the theory in question, the Kerr metric, the SymPy software, and the computational procedures used. The aim of the work is to calculate the energy of spacetime for the Kerr metric using the symbolic mathematics software SymPy. The primary hypothesis is that the energy of Kerr spacetime, calculated in SymPy within the framework of the general teleparallel equivalent of general relativity, is proportional to the mass. The secondary hypothesis is that, in Kerr-Schild coordinates, the canonical energy-momentum tensor vanishes if the affine connection is also equal to zero.

Speaker: Roald Heinrich Ivask (University of Tartu)

Kerr_s_spacetime_energy___Tartu_2025.pdf

14:40 Warp drives in scalar-tensor theories

Spacetime configurations corresponding to warp drives allow observers to traverse distances faster than the speed of light without violating the postulates of special relativity. Although appealing for space travel, it has been shown that warp drives in general relativity require exotic matter that violates energy conditions. Cosmological observations bring out the shortcomings of general relativity due to which many modified theories of gravity have been proposed. In this talk we explain how to build upon the previous results in general relativity and study warp drives in scalar-tensor theories of gravity in order to find whether warp drives are possible without introducing ghost fields or exotic matter. We present first steps in solving the problem by mapping out a tree of solutions based on various assumptions. Considering additional assumptions we analyse the branches of the tree and the physical problems that arise.

Speaker: Joosep Lember (University of Tartu)

Lember_GeomGrav_2025.pdf

13:30 → 15:05 Monday Parallel 2 - A101

13:30 Quintessential inflation in Palatini F(R,X) gravity

Palatini $F(R,X)$ gravity, with $X$ the inflaton kinetic term, proved to be a powerful framework for generating asymptotically flat inflaton potentials. Here we show that a quadratic Palatini $F(R,X)$ restores compatibility with data of the Peebles-Vilenkin quintessential model. Moreover, the same can be achieved with an exponential version of the Peebles-Vilenkin potential if embedded in a Palatini $F(R,X)$ of order higher than two.

Speaker: Christian Dioguardi (NICBP)

Quintessential_inflation_in_F_R_X____Presentation.pdf

13:55 The formulation interpolation: the quasi-Palatini approach to modified gravity

Distinct formulations of nonminimal models have been a leading motivating factor for the development of alternative theories of gravity. The metric and Palatini formulations, understood to be equivalent in minimally coupled models, can lead to physically distinct theories when a nonminimal coupling is introduced. The choice of formulation, made before the action is written down, is a discrete one, and it is therefore interesting to consider the possibility of interpolating between the resulting actions in order to arrive at a continuous class of theories. As such, we propose the "quasi-Palatini" formulation, which gives rise to a family of scalar-tensor theories with distinct observational signatures indexed by a single parameter that measures the relative "Palatininess" of the model. We demonstrate that this approach can be used to enhance the robustness of nonminimal models such as Higgs inflation, and that it can be used to motivate the pole structure inherent in alpha-attractors. We finally discuss how this interpolation may be extended to teleparallel theories, and how the relative strength of the boundary terms gives rise to hyperformulations of the same underlying model with distinct physics.

Speaker: Sotirios Karamitsos (University of Tartu)

GeomGrav25_talk_Quasi_Palatini_Karamitsos.pdf

14:20 Global Portraits of Inflation in Nonsingular Variables

In the phase space perspective, scalar field slow roll inflation is described by a heteroclinic orbit from a saddle type fixed point to a final attractive point. In many models the saddle point resides in the scalar field asymptotics, and thus for a comprehensive view of the dynamics a global phase portrait is necessary. For this task, in the literature one mostly encounters dynamical variables that either render the initial or the final state singular, thus obscuring the full picture. In this work we construct a hybrid set of variables which allow the depiction of both the initial and final states distinctly in nonsingular manner. To illustrate the method, we apply these variables to portray various interesting types of scalar field inflationary models like metric Higgs inflation, metric Starobinsky inflation, pole inflation, and a nonminimal Palatini model.

Speaker: Dmitri Kraiko (University of Tartu)

14:40 Testing non - metricity based gravity models against cosmological data.

We investigate non-metricity-based gravity models through a model-independent framework, confronting them with recent observational data. Employing Bayesian statistical methods, we analyze late time background evolution using DESI-BAO and Supernovae data, and probe linear perturbations via the modified gravity functions, effective gravitational coupling and damping in the gravitational wave propagation. We derive constraints on the model parameters and systematically map several popular non-metricity gravity models onto our parameter space.

Speaker: Purnendu Karmakar (University of Tartu)

PPT_FQ_Log_Tartu_2025_06_30.pdf

15:05 → 15:40 Coffee Break

15:40 → 17:20 Monday Parallel 3 - A106

15:40 Ghosts and strong coupling in Bimetric MOND

Modified Newtonian dynamics (MOND) is a phenomenological theory which aims to explain dark matter. However, the theory is criticized for not being a good fit to observations at multiple scales and with lack of fundamental motivations. Bimetric MOND (BIMOND) is a theory with a fundamental relativistic action including two copies of Eintein-Hilbert terms (each equiped with a separate dynamical metric) and a function of a scalar constructed through contorsion (the difference of the two Levi-Civita connections). In this talk I will show that this theory is in fact not viable as a fundamental theory. This is shown through perturbation theory around Minkowski and Hamiltonian analysis around a very simple background.

Speaker: Daniel Blixt

Tartu25BIMOND.pdf

voicu_presentation_tartu.pdf

16:05 Propagation of gravitational waves in general quadratic teleparallel gravity theories

General theory of relativity, which is currently the widely accepted theory of gravity, directly predicts the existence of gravitational waves. This phenomenon was directly measured only in 2015 and in 2017 observational data confirmed the prediction that gravitational waves propagate at the speed of light. However, there are phenomena that general relativity cannot satisfactorily explain without introducing problematic concepts such as dark matter and dark energy. This has led us towards the investigation of alternative theories of gravity. One such group of theories is the general quadratic teleparallel theories of gravity, where gravity results from the torsion and non-metricity of space. Studying the propagation of gravitational waves in such theories helps assess the viability of these theories. In this talk I will present my Master's thesis, where formulas describing the speed and polarisations of gravitational waves in general quadratic teleparallel theories of gravity were derived. Furthermore, different cases of this group of theories were separately examined and analysed to see what happens with different sets of constants.

Speaker: Kärt Soieva (University of Tartu)

GravWaves_QuadTele_Soieva.pdf

16:30 Regularisation of the action and its non-uniqueness in the Euclidean teleparallel gravity

We investigate the regularization of the Euclidean gravitational action in the teleparallel equivalent of general relativity (TEGR), where the action is dynamically equivalent to that of GR but depends on both the tetrad and an undetermined spin connection. We evaluate the action using both bulk and quasi-local surface integrals across three frames: proper, canonical, and a newly introduced Euclidean free-falling frame. While all yield finite action, the results differ, revealing a fundamental non-uniqueness. In particular, the Euclidean free-falling frame admits an infinite family of inequivalent finite action solutions, raising important questions about the interpretation and regularization of gravitational actions in teleparallel geometry.

Speaker: Michal Stano (Institute of Mathematics of the Czech Academy of Sciences)

Stano_Tartu.pdf

16:55 Black holes, horizons and tetrads in New General Relativity

Due to GR's age as a theory, many coordinate systems have been developed for it, each of which is specialized for some particular application. However, extensions of GR often lack these coordinate systems, as the GR ones are not trivially generalizable. In this thesis, we seek to develop such coordinate systems for New General Relativity (NGR), specifically in the context of black hole analysis and taking inspiration from known systems in GR. By making use of such coordinate systems, one may gain better insights into the geometric properties of black holes, such as the properties of horizons. In addition, one may analyze the mathematical properties of the tetrad of the black hole spacetime, which, as the basic dynamical object of NGR, opens up more avenues of research into black holes in NGR. We develop three coordinate systems for 1-parameter NGR, based on the Kruskal-Szekeres, Eddington-Finkelstein and Gullstrand-Painlevé coordinates from GR. We find that the 1PNGR version of the KS metric can be obtained both through a coordinate transformation of a known Schwarzschild-like solution and also from a completely new "KS-like" solution, the tetrad of which is non-singular at the horizon under a certain choice of parameters. However, this same solution is asymptotically complex and therefore the corresponding spacetime cannot be defined on the entire coordinate space. For the EF and GP coordinates, we find that the same is possible, but the new tetrads do not satisfy the field equations, except for zero-mass cases. In addition, the tetrads in these coordinates are inevitably singular at the horizon. Due to the possibility of these coordinate transformations, all systems present a Killing, Cauchy, and apparent horizon at r=2M.

Speaker: Paul Martin Kull (University of Tartu)

Presentation.pdf

15:40 → 17:20 Monday Parallel 4 - A101

15:40 $\tilde\xi$-attractors in metric-affine gravity

We propose a new class of inflationary attractors in metric-affine gravity. Such class features a non-minimal coupling $\tilde\xi \, \Omega(\phi)$ with the Holst invariant $\tilde {\cal R}$ and an inflaton potential proportional to $\Omega(\phi)^2$. The attractor behaviour of the class takes place with two combined strong coupling limits. The first limit is realized at large $\tilde\xi$, which makes the theory equivalent to a $\tilde {\cal R}^2$ model. Then, the second limit considers a very small Barbero-Immirzi parameter which leads the inflationary predictions of the $\tilde {\cal R}^2$ model towards the ones of Starobinsky inflation. Because of the analogy with the renown $\xi$-attractors, we label this new class as $\tilde\xi$-attractors.

Speaker: Antonio Racioppi (National Institute of Chemical Physics and Biophysics (EE))

Racioppi_GFG2025.pdf

16:05 On the geometric origin of the energy-momentum improvement terms

I will show how the Belinfante-Rosenfeld improvement terms, that render the energy-momentum tensor symmetric, emerge by coupling the matter to the affine-connection. In this sense the improvement terms correspond to the hypermomentum of matter. I will show how this is realized in two standard examples, the Maxwell field and the Dirac field. I will also show how the connection-matter couplings can also result in a traceless energy tensor when the theory is invariant under frame rescalings, by revisiting the known example of a comformally invariant scalar field. Generalizations to higher derivative theories will also be discussed

Speaker: Damianos Iosifidis (University of Tartu, Scuola Superiore Meridionale)

Geometric_Origin_Tartu_Conference (3).pdf

16:30 Friedmann cosmology with hyperfluids

In metric-affine gravity, both the gravitational and matter actions depend not just on the metric, but also on the independent affine connection. Thus, matter can be modeled as a hyperfluid, characterized by both the energy-momentum and hypermomentum tensors. The latter is defined as the variation of the matter action with respect to the connection, and it encodes extra (micro)properties of particles. For a homogeneous and isotropic universe, it was recently shown that the generic cosmological hypermomentum possesses five degrees of freedom: one in dilation, two in shear, and two in spin part. In this presentation, we discuss the implications of this perfect hyperfluid on the universe with the Friedmann-Lemaître-Robertson-Walker metric. We adopt a simple model with non-Riemannian Einstein-Hilbert gravitational action plus arbitrary hyperfluid matter, and solve analytically the cosmological equations for single and multiple component hypermomentum contributions using different assumptions about the equation of state. It is remarkable, that in a number of cases the forms of the time evolution of the Hubble function and energy density still coincide with their general relativity counterparts, only the respective indexes $w_{\mathrm{eff}}$ and $w_{\rho}$ start to differ due to the hypermomentum corrections. The results and insights we obtained are very general and can assist in constructing interesting models to resolve the issues in standard cosmology.

Speaker: Margus Saal (University of Tartu)

geomgrav_2025_saal.pdf

16:55 Internal gauge structure and ghost instabilities in general torsion theories

We analyze which internal affine gauge transformations can be attributed to the torsion, focussing on those that tensor give rise to Lie algebras. We find two such non-trivial structures, in which the gauge parameters are a two form and a scalar. In the first case gauge invariant variables are singled out, and a higher derivative power-counting renormalizable invariant action is derived. The Lagrangian depends on four free parameters, and a stability analysis shows that it is free from ghost instabilities in Euclidean signature, though we find a tachyonic scalar mode.

Speaker: Dr Dario Sauro (Theoretical Physics Institute University ofJena)

presentation-DS-Tartu2025.pdf

18:30 → 22:30 Reception

Tuesday 1 July

09:15 → 10:05 Finsler Geometry and the Fabric of Spacetime

Finsler spacetime geometry offers a natural generalization of Lorentzian one, based on a most general notion of arc length. In this talk, I will discuss:

• The physical motivations for adopting a Finslerian model of spacetime, with emphasis on its potential to describe scenarios beyond the reach of Riemannian geometry.
• The overlap between Finsler gravity and metric-affine gravity -- and the way the two frameworks enrich each other.
• A concrete Finslerian model for the gravitational field which leads, in cosmological symmetry, to an exponentially expanding spacetime, without the need of a cosmological constant or of any additional quantities.

Speaker: Nicoleta Voicu (UniTBV)

10:05 → 10:35 Coffee Break

10:35 → 11:00 Bounding anisotropic Lorentz Invariance Violation

Observations of energy-dependent photon time delays from distant flaring sources provide significant constraints on Lorentz Invariance Violation (LIV). Such effects originate from modified vacuum dispersion relations, causing differences in propagation times for photons emitted simultaneously from gamma-ray bursts, active galactic nuclei, or pulsars. These modifications are often parametrized within a general framework by an effective quantum gravity energy scale $E_{QG,n}$. While such general constraints are well established in the LIV literature, their translation into specific coefficients of alternative theoretical frameworks, such as the Standard-Model Extension (SME), is rarely carried out. In particular, existing limits on the quadratic case ($n=2$) of $E_{QG,n}$ can be systematically converted into constraints on the non-birefringent, CPT-conserving SME coefficients $c^{(6)}_{(I)jm}$.

Speaker: Merce Guerrero (University of Aveiro)

LIV.pdf

11:00 → 11:25 Weak equivalence principle and nonrelativistic limit of general dispersion relations

We study the weak equivalence principle in the context of modified dispersion relations, a prevalent approach to quantum gravity phenomenology. We find that generic modified dispersion relations violate the weak equivalence principle. The acceleration in general depends on the mass of the test body, unless the Hamiltonian is either 2-homogeneous in the test particles’ 4-momenta or the corresponding Lagrangian differs from the homogeneous case by a total derivative only. The key ingredient of this calculation is a 3 + 1 decomposition of the parametrization-invariant relativistic test particle action derived from the dispersion relation. Additionally, we apply a perturbative expansion in the test particle’s spatial velocity and the inverse speed of light. To quantify our result, we provide a general formula for the Eötvós factor of modified dispersion relations.

Speaker: Christian Pfeifer (University of Bremen, ZARM)

MDRsWEP_GeomGrav2025.pdf

11:25 → 11:50 Finsler geometry as a window to Planck scale physics

We discuss the problem of describing the effective quantum spacetime probed by a high energetic particle by Finsler Geometry. We highlight the main theoretical gains and challenges of this approach in quantum gravity.
We also discuss the use of present and future experiments and observations to constrain Finslerian departures of Riemannian Geomety at the Planck scale and the prospects for future tests.

Speaker: Iarley Lobo (Federal University of Lavras)

Iarley-Tartu.pdf

11:50 → 13:30 Lunch

13:30 → 15:05 Tuesday Parallel 1 - A106

13:30 Variationality and Finsler metrizability of nonmetric autoparallels

In alternative theories of gravity, particles may follow either Riemannian geodesics or non-Riemannian autoparallels, depending on the presence of a geometry-matter coupling via hypermomentum. Typically, autoparallels associated with connections that have nonmetricity are not derived from a variational principle. In this talk, we take the first steps toward finding a Finslerian variational principle, by rewriting the autoparallel equation as a Finslerian geodesic. Specifically, we provide the first steps toward constructing a Finsler $(\alpha,\beta)$ Lagrangian, which metrizes certain connections with vectorial nonmetricity.

Speaker: Lehel Csillag (UBB, UniTBV)

Csillag_Talk_Tartu.pdf

13:55 Local Symmetries of Finsler Gravity and Its Dynamics

Finsler spacetimes are constructed such that they deliver a causal structure on the set of events, give a definition of observers as well as their measurements and encode the gravitational dynamics. In my master thesis “Local Symmetries of Finsler Gravity and its Dynamics” I focus on the notion of observers with the overall goal of determining the possible observer transformations. In a short talk I would like to summarise first results of my research: At the beginning I define the notion of local symmetry transformations of Finsler spacetimes and introduce one possible generator for such symmetries. I then analyse the algebraic structure of this candidate and have a look at its specific form in the case of (α,β)-metrics. Furthermore, I examine the Lie derivatives of the fundamental building blocks of the geometry defined by the n-th partial derivatives of the Finsler-Lagrange function.

Speaker: Lea Zybur

Tartu_presentation_LZybur.pdf

14:20 Generalized Geodesic Equations from Planck Scale Deformed Dispersion Relations

Modified dispersion relations gives an effective way to incorporate Planck-scale effects into particle kinematics and quantum gravity phenomenology. These effects can be encoded in Hamilton functions and it goes beyond the standard quadratic dependence on the four-momentum. This leads to nontrivial modifications in the geodesic equations for point particles. In this talk, I explore the consequences of a broad class of deformed Hamiltonians of the form $H(x,p) = H(g(p,p),A(p))$ , where $g(p,p) = g^{ab}(x)p_a p_b$ and $A(p) = A^a(x)p_a$ which generalize both Finsler-type and kappa-Poincaré-inspired models.
My goal is to understand how these Hamiltonians modify the usual geodesic equations that describe the motion of point particles. By reinterpreting Hamilton’s equations geometrically, I show how the additional structure, especially the linear momentum term, gives rise to corrections that could capture quantum gravitational effects in a covariant way. This provides a flexible and powerful framework to describe particle propagation on curved spacetimes and gives a way to connect these models to future observations.

Speaker: Zubaida Karim Juthy (University of Bremen)

Presentation (1).pptx

14:40 Algebraic classification of the gravitational field in general metric-affine geometries

We present the full algebraic classification of the gravitational field in four-dimensional general metric-affine geometries. As an immediate application, we determine the algebraic types of the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity.

Speaker: Jorge Gigante Valcarcel (Institute for Basic Science)

13:30 → 15:00 Tuesday Parallel 2 - A101

13:30 Gauge theory, gravity, and nontrivial constitutive laws

In BF-theory terms, apart from the structure group itself, gravity and Yang-Mills theory or electromagnetism are distinguished in the constitutive law, or the simplicity constraints. This is suggestive of a unified topological phase, which is broken into separate internal and external gauge theory, with clear, almost canonical preferences for the excitation B-field for either part. But what if one component has a modified constitutive law? As the interactions are independent, there should be no effect. We will consider how to formalize this in terms of a constitutive diagram, alongside a discussion of spontaneous simplicity constraints, a heuristic description of internal and external gauge theory, and a geometric issue for the unified phase of spacetime.

Speaker: Priidik Gallagher (University of Tartu)

Gallagher_Geomgrav2025.pdf

13:55 Chiral gauge theory of gravity and dark matter

Lorentz gauge theory of gravity with a symmetry breaking "Cartan khronon" field demonstrates its successful explanation for the $\Lambda$CDM model, with an emergent integration 3-form behaving as ideal dust. Within the chiral scheme of this theory, only the right-handed regime recovers the general relativity. A natural question that arises is what happens with the left-handed gravity? When both right- and left- handed gravity are included, we find the integration 3-form is essential to formulate non-trivial cosmology. This talk discusses cosmology based on both-handed gauge theory of gravity and why the integration 3-form is a compelling dark matter candidate.

Speaker: Lucy Zheng (University of Tartu)

GeomGrav2025.pdf

14:20 Strong hyperbolicity in teleparallel gravity

We review the current state of the numerical relativity formalism for teleparallel theories of gravity and assess the hyperbolicity of the 3+1 decomposition of the equations of motion in the Hamiltonian formulation. For this, we analyse a simplified version of the analog to the ADM equations in the teleparallel equivalent of general relativity. We consider linear perturbations around a flat spacetime and impose these conditions in the tetrad and its conjugate momenta. We present the form of the 3+1 equations of motion and outline the procedure in order to consistently study their hyperbolicity properties.

Speaker: Cheng Cheng (King's College London)

Strong Hyperbolicity.pdf

14:40 Well-posed evolution and gravitational collapse of self-interacting vector fields

Dynamical evolution of self-interacting vector fields often faces instabilities and apparent pathologies when performing numerical simulations. By displaying a detailed analysis of the initial-value problem of the theory in the language of scalar-tensor theories, I will show that the former are actually due to the breakdown of the hyperbolicity of the theory (Tricomi-type or Keldysh-type). I will also give numerical evidences that these issues can be avoided by means of the “fixing-the-equations” approach, enabling stable numerical evolutions in spherical symmetry. Finally, I will report on initial configurations for the massive vector field leading to gravitational collapse and the formation of black holes, for a particular class of self-interactions in which no "pathologies" take place.

Speaker: Dr Marcelo Rubio

15:05 → 15:40 Coffee Break

15:40 → 17:20 Tuesday Parallel 3 - A106

15:40 Teleparallel gravity from the principal bundle viewpoint

Since General Relativity is a classical gauge gravitational theory of diffeomorphisms, a natural question arises: does the same hold for TEGR?
In this talk, we explore the gauge structure of TEGR from the perspective of principal bundles. We also focus on the popular claim that TEGR can be viewed as a gauge theory of translations. It is explained that the standard way of approaching this claim, using the principal T(4)-bundle endowed with a translational connection, leads to inconsistencies. We suggest an alternative approach based on the affine group and affine bundles with affine connections, resulting in a consistent formulation of TEGR.

Speaker: Sebastian Brezina (Comenius University in Bratislava)

Teleparallel_gravity_from_the_principal_bundle_viewpoint.pdf

16:05 The classification of general affine connections in Galilei geometry: towards metric-affine Newton–Cartan gravity

Galilei geometry, which may be obtained as a degenerate limit of Lorentzian geometry, allows for a coordinate-free formulation of Newtonian gravity, called Newton–Cartan gravity. This enables a geometric understanding of the Newtonian $c\to\infty$ limit of standard general relativity (GR). Recently, analogous geometric descriptions of the Newtonian limits of the (metric) teleparallel equivalent of GR (TEGR) and the symmetric teleparallel equivalent of GR (STEGR) have been developed.

In this talk, we will discuss the classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This classification lays the foundation for the discussion of generic metric-affine geometric formulations of Newtonian gravity. Our result generalises the well-known case of (torsional) connections compatible with the metric structure of the Galilei manifold.

Similarly to the well-known pseudo-Riemannian case, the additional freedom for connections that are not metric-compatible lies in the covariant derivatives of the two tensors defining the metric structure (the clock form and the space metric). However, differently to the non-degenerate pseudo-Riemannian case, these two non-metricities are not fully independent of each other.

Speaker: Philip Schwartz (Leibniz Universität Hannover, Institut für Theoretische Physik)

Talk_Classification_connections_Schwartz_GeomGrav_2025.pdf

16:30 A Directive for deriving (Algebraically) General Solutions of Einstein’s Equations based on the Canonical Killing Tensor Forms

This work serves as a sequel to our previous study, where, by assuming the existence of the canonical Killing tensor forms and applying a general null tetrad transformation, we obtained a variety of solutions (Petrov types D, III, N) in vacuum with cosmological constant $\Lambda$. Among those, there is a unique Petrov type D solution with a shear-free, diverging and non-geodesic null congruence which will be presented in full detail in the following sections. Additionally, in this work we will introduce a Petrov type I solution with a shear-free, diverging and non-geodesic null congruence, obtained by employing Lorentz transformations, within the concept of symmetric null tetrads, instead of the general null tetrad transformation. Building upon this and in line with the concept of symmetric null tetrads, which played a crucial role in deriving the most general Petrov type D solution ( Debever-Plebanski-Demianski solution), we propose a new directive. This directive suggests that, by assuming the canonical forms of Killing tensor and implying Lorentz transformations correlating the spin coefficients between themselves ($\pi=-\bar\tau, \kappa = - \bar\nu$, etc.) can yield a broader class of (algebraically) general solutions to Einstein's equations, rather than relying on boosts and spatial rotations.

Speaker: Dionysios Kokkinos (Hellenic Mediterranean University)

Conf_Pres.pdf

16:55 The Maldacena-Shenker-Stanford Conjecture in General Relativity and beyond

The Maldacena-Shenker-Stanford (MSS) conjecture establishes the existence of an upper bound to the Lyapunov exponent of a thermal quantum system with a large number of degrees of freedom.
Holographic calculations of out-of-time order correlation functions (OTOCs), which are conveniently employed as indicators of the magnitude of quantum chaos, motivate such a statement, leading to the identification of black holes as the fastest scramblers in nature.
This talk aims to give an insight into the universality of the MSS conjecture. We claim that it can be violated in various metric $f(R)$ gravity models as a consequence of the propagation of metric instabilities in a degenerate Schwarzschild-de Sitter background. Then, following a detailed investigation of the Extended Geometric Trinity of Gravity, a set of three dynamically equivalent theories arising from an ad-hoc extension of the corresponding constituting theories of the Trinity of Gravity (namely General Relativity, the Teleparallel Equivalent to General Relativity, and the Symmetric Teleparallel Equivalent to General Relativity), we conclude that the violation occurs independently of the conferred representation of gravity in such a framework.

Speaker: Sara Cesare (Scuola Superiore Meridionale)

GoemGrav 2025.pdf

15:40 → 17:20 Tuesday Parallel 4 - A101

15:40 Geometry of Disformal Transformations

Disformal transformations are specific deformations of the metric, involving other fields and their derivatives. They have been used to relate different modified gravity models. For instance, mimetic and teleparallel gravities.

We will put forward a geometric formulation of disformal transformations, thereby elucidating the role of the non-metric fields therein. We will also identify key properties for disformal transformations that guarantee physical equivalence between the connected theories.

Speaker: Jordi Gaset Rifà (CUNEF Universidad)

GasetGeomDisformal.pdf

16:05 Chiral signatures from the Barbero–Immirzi parameter in inflationary tensor modes

The Ashtekar connection-based approach of general relativity offers a compelling avenue for re-examining gravitational dynamics, particularly through its Hamiltonian formulation. This framework introduces the Barbero–Immirzi parameter, a factor whose role varies between classical and quantum treatments.

Classically, the Barbero–Immirzi parameter does not appear in the equations describing the propagation of gravitational waves. However, depending on the chosen quantization scheme, this parameter can crucially influence vacuum fluctuations of tensor modes during inflation, most notably by inducing chiral asymmetries.

In this talk, I will examine both classical and quantum scenarios within the context of non-minimal inflationary models, which are increasingly supported by observations. The focus will be on the behavior of propagating tensor modes and their potential imprints on the observational data.

Speaker: Mehraveh Nikjoo

16:30 On the quantum equivalence between Teleparallel Gravity and GR

In this talk I will show our recent work on the quantization of Teleparallel Gravity (or TEGR), which is classically equivalent to GR. I compute the quadratically divergent counterterms that arise in the action, showing that they break the equivalence with GR at the quantum level. I then compute the logarithmically divergent counterterms and discuss their implications.

Speaker: Davide Zarrilli

On the quantum equivalence between Teleparallel Gravity and GR.pdf

16:55 Causality and Stability from the Acoustic Metric

Scalar-tensor theories with derivative interactions form backgrounds which spontaneously break Lorentz invariance (cosmology during inflation or the dark energy era is the archetype). I will discuss how to think about the dynamics of free scalar perturbations, phonons, on general anisotropic backgrounds, showing that phonons move on null geodesics of an acoustic spacetime described by its own metric and own connection. This acoustic metric and its inverse give the dispersion relation, rays and phase velocities and construct two sound cones. The acoustic connection features non-metricity with respect to the usual spacetime.

I will discuss how to read off true instabilities, ghosts and gradient instabilities, from the invariant properties of the acoustic metric, but also discuss false instabilities that may appear for some observers, relating this to Cherenkov radiation and the ill-posedness of the Cauchy problem.

Speaker: Ignacy Sawicki (CEICO, Institute of Physis, Czech Academy of Sciences)

Sawicki_Acoustic.pdf

18:15 → 19:15 From stars and seismic waves to the fundamentals of gravity

We will explore the nature of gravity and the modern physics tools that enhance our understanding of this fundamental force. By studying remarkable objects such as neutron stars and white dwarfs, we gain access to natural laboratories where gravitational theories can be tested under extreme conditions, revealing the interplay of fundamental interactions. In addition, we will examine other astrophysical objects, including those closer to us, such as the Sun, Earth, and the planets of our Solar System. These familiar celestial bodies have become promising candidates for investigating the intricacies of gravity and its potential quantum corrections. Through their study, we uncover the phenomena that challenge the classical descriptions and open pathways to a deeper understanding of gravitational physics and other fundamental interactions. Notably, seismic waves seem to carry vast amounts of untapped information that has yet to be thoroughly explored. This comprehensive exploration, spanning distant stellar remnants to the planets in our cosmic neighborhood, provides a rich perspective on gravity and its role in shaping the universe.

Speaker: Dr Aneta Wojnar (Tartu University)

Wednesday 2 July

09:15 → 10:05 Joining black hole imaging and ringdown: A novel view of testing gravity

In geometric-optics limits, there exists a mapping between black hole images and eikonal black hole quasinormal modes (QNMs). More explicitly, the real part and imaginary part of the QNM frequencies correspond to the ring size and the detailed ring structure of the image, respectively. The explicit identification of such eikonal correspondence, however, relies a lot on the symmetry of the spacetime under consideration and, therefore, is highly non-trivial. Having in mind that such a correspondence may be violated beyond GR, I will discuss how joining the observations of ringdown and images of black holes could test such correspondence and constrain a class of non-GR theories where the correspondence is broken, opening a novel window of testing gravity.

Speaker: Che-Yu Chen (iTHEMS, RIKEN)

2025Tartu.pdf

10:05 → 10:35 Coffee Break

10:35 → 11:00 No vacuum? No problem!

In spite of their unequivocal potential and the increasing number of counterexamples, ghost-ridden theories remain eminently disregarded as necessarily unphysical. In this talk, we will being by providing a lightning review of the problematic, and troubleshooting proposals in the literature. Then, we will present our own recent constructive method to avoid catastrophe in the face of a ghost*. This not only encompasses all prior results, but also extends them in a consequential and counter-intuitive manner.

*Terms and conditions apply.

Speaker: Prof. Verónica Errasti Díez

11:00 → 11:25 Imaging black holes and horizonless compact objects

We present the theoretical and phenomenological basis of the imaging of astrophysical objects compact enough to hold a photon sphere, namely, an unstable bound light orbit. We discuss the features of the two most salient features of such an imaging (the photon rings and the shadow) for black holes and horizonless compact objects alike and comment on the possibilities and difficulties within this field as supplied by very-long baseline interferometry technologies.

Speaker: Prof. Diego Rubiera-Garcia (Complutense University of Madrid)

Imaging black holes and horizonless compact objects.pdf

11:25 → 11:50 Gravitational wave propagation in hybrid metric-Palatini gravity

In this work we analyze the propagation properties of gravitational waves in the hybrid metric-Palatini gravity theory. We introduce the scalar-tensor representation of the theory to make explicit the scalar degrees of freedom of the theory and obtain their equations of motion in a form decoupled from the metric tensor. Then, we introduce linear perturbations for the metric tensor and for the two scalar fields and obtain the propagation equations for these three quantities. We analyzed the theory both at non-linear and at linear level through the Newman-Penrose formalism so to find the polarization states. We show that the tensor modes propagate at the speed of light and feature the usual $+$-- and $\times$--polarization modes also present in General Relativity (GR), plus two additional polarization modes: a longitudinal mode and a breathing mode, described by the same additional degree of freedom. On the other hand, the theory features two additional scalar modes not present in GR. These modes are massive and, thus, propagate with a speed smaller than the speed of light. The masses of the scalar modes depend solely on the interaction potential between the two scalar fields in the theory, which suggests that one can always fine-tune the potential to make the scalar modes massless and reduce their propagation speed to the speed of light. This feature potentially renders the theory unfalsifiable in the context of gravitational wave propagation.

Speaker: João Luís

João Rosa Talk.pdf

11:50 → 13:30 Lunch

13:30 → 21:30 Excursion

Thursday 3 July

09:15 → 10:05 4D GR via triples of 2-forms

I will describe a formalism, originally envisaged in the 1960s and 1970s, that reformulates four-dimensional General Relativity in terms of a triple of 2-forms rather than a metric. In this approach, the field equations are expressed using the exterior derivative acting on differential forms, bringing the theory structurally closer to electromagnetism than in the conventional metric formulation.
This formalism has several attractive features. The restriction to the self-dual sector of gravity becomes especially natural, and the Gravity = (Yang-Mills)² relation—connecting the self-dual sectors of the two theories—emerges transparently. The formalism also provides an excellent framework for perturbative computations of gravitational scattering amplitudes and leads to a remarkably compact reformulation of the Einstein equations. For instance, verifying that the Kerr black hole metric solves the field equations can be done entirely by hand within this framework.

Speaker: Kirill Krasnov (University of Nottingham)

triples-2-forms-tartu.pdf

10:05 → 10:35 Coffee Break

10:35 → 11:00 On the Gravitational Foundations of Geometry

Although Newton published a theory of gravitation in his Principia (1687), the birth of modern science of space and time might be traced to Kant's insight in the 18th century - rooted in what we could nowadays call spontaneous breaking of chiral symmetry - that led him to realise Euclidean space and time as categories of intuition.

In the 19th century, Riemann and Clifford reimagined gravitation and matter as manifestations of geometry and curvature, connecting physical phenomena to the structure and dynamics of space. Clifford's algebra already laid the mathematical groundwork for the unification of space and time - and, of the chiral aspects of geometry.

The 20th century brought quantum mechanics, which eventually suggests an
informational view, with space and time as fundamental cognitive organising principles agreeing with Kant's utterly compelling conclusions. The basic units are bits, which because they are quantum-mechanical, are qubits. Moreover, because the world is only intelligible to us in space and in time, the atoms of information are gauged qubits - representable as spinors, subject to Clifford's algebra.

This perspective finds its most complete physical expression in the recently discovered gauge theory of spacetime and gravity, the grandest breakthrough of at least the 21st century.

(To those inclined to note earlier gauge-theoretical formulations of gravity: please consult footnotes 1 and 2 of https://inspirehep.net/literature/2721983 carefully.)

Speaker: Tomi Koivisto (University of Tartu)

GFoG25.pdf

11:00 → 11:25 Removing spurious degrees of freedom from EFT of gravity

Effects of ultraviolet completions of gravity can be captured in low-energy regimes by local higher curvature corrections. Such description, however, is limited to yield strictly perturbative corrections, due to unphysical Ostrogradsky instabilities induced by higher derivatives in the correction terms. I will present a procedure for expunging spurious degrees of freedom from effective theories of gravity, and casting them as lower-derivative theories that capture all the information about the corrections, but propagates only the massless spin-2 graviton degree of freedom. Resulting reduced theories fall under the category of Minimally modified gravity theories, that preserve spatial diffeomorphisms, but modify temporal diffeomorphisms in a way that preserves the constraint structure. Such theories are free from Ostrogradsky instabilities, and can be used to study the ultraviolet effects self-consistently.

Speaker: Dražen Glavan (CEICO, Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic)

Glavan_Tartu.pdf

11:25 → 11:50 Primordial Black Holes, Extremality, and Dark Matter: Rethinking Evaporation Limits

Earlier studies investigating the allowed fraction of dark matter as primordial black holes (PBHs) tend to completely rule out PBHs with masses smaller than ~10⁻¹⁵ solar masses. This is due to the lack of evidence for Hawking radiation coming from the final evaporation stages of such small PBHs. These limits, however, make the key assumption that these PBHs can be modelled as uncharged, non-rotating Schwarzschild black holes. Extending either the modell of particle physics or of gravity can easily allow for a range of extremal black holes, that behave fundamentally differently in this regard. In this talk, we will present changes to these lower mass bounds when charge is included, i.e., by going to Reissner–Nordström black holes as models for PBHs. Concretely, we will add a "dark" U(1) charge, present in the early universe when the PBHs was formed; while not present in today's universe, it might still appear as a black hole charge. We use the Hiscock and Weems model of charged black hole evaporation, to correctly include the Schwinger effect. We then investigate and present the updated mass bounds for PBHs as dark matter candidates and their dependence on mass and charge of the corresponding "dark" electrons.

Speaker: Sebastian Schuster (Stockholm University)

2025-05-SeSc-GeomGrav.pdf

11:50 → 13:30 Lunch

13:30 → 13:55 Quasinormal modes and absorption cross-section of a Bardeen black hole in presence of perfect fluid dark matter

In this talk, we explore the quasinormal modes (QNMs) and absorption cross sections of the $(3+1)$-dimensional Bardeen black hole spacetime surrounded by perfect fluid dark matter. While the case of massless scalar field perturbations has been previously addressed, our analysis focuses on two less explored scenarios: massive scalar field perturbations and massless Dirac field perturbations.

To compute the QN frequencies, we apply the semi-analytical WKB method up to third order. For consistency and validation, we also use the Pöschl-Teller approximation and compare the results across both approaches.

Our analysis considers variations in three key parameters of the model: the mass of the scalar field $\mu$, the dark matter parameter $\alpha$, and the magnetic charge $g$. The computed QN frequencies are presented in tables and plots for clarity.

In the second part of the study, we compute the absorption cross section using the third-order WKB method. Specifically, we evaluate the reflection and transmission coefficients as well as the partial absorption cross sections. The results, presented graphically, illustrate how the dark matter parameter $\alpha$ and the scalar field mass $\mu$ influence these quantities.

Speaker: ANGEL RINCON RIVERO (Universidad de Alicante)

Talk_GFG_2025_v1.pdf

13:55 → 14:20 Black holes and naked singularities in four dimensional dS and AdS Chamseddine gravity

We analyze solutions of Chamseddine's topological gravity in four space-time dimensions and discover various black hole solutions with(out) torsion as well as those that describe naked singularities. Because all of the solutions belong to the sector with vanishing scalar fields, they share peculiar trait that all conserved charges are vanishing.

Speaker: Branislav Cvetković (Institute of physics, Belgrade)

cvetkovic.pdf

14:20 → 14:50 Coffee Break

14:50 → 16:20 Plenary Discussion

GeomGrav2025_Discussion.pdf

Summary2025_1.jpeg

Summary2025_2.jpeg

Summary2025_3.jpeg

19:00 → 22:00 Conference Dinner

Friday 4 July

09:30 → 10:00 Morning Coffee

10:00 → 10:20 Introducing Cadabra, a field-theory motivated approach to symbolic computer algebra

The Cadabra symbolic computer algebra system is an open source tool designed specifically for problems in field theory. It has extensive functionality for tensor computer algebra, tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, component computations, implicit coordinate dependence, multiple index types and many more. The input format is a subset of TeX.

I will present an overview-level introduction for beginners to this system, starting with a discussion of the history behind it, the problems that inspired it, and its relation to other systems, in particular SymPy. I will then focus on some more recent additions which have made Cadabra a more generally useful tool in symbolic (and now also numeric!) computing, and give a brief outline of future directions.

Speaker: Kasper Peeters (Durham University)

10:20 → 12:00 Cadabra Workshop

Convener: Dražen Glavan (CEICO, Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic)

Cadabra_tutorial.pdf

12:00 → 13:30 Lunch

13:30 → 14:20 Emergent Gravity from Topological Quantum Field Theory: Stochastic Gradient Flow Perspective away from the Quantum Gravity Problem

We propose a scenario according to which the ultraviolet completion of General Relativity is realized through a stochastic gradient flow towards a topological BF theory. Specifically, we consider the stochastic gradient flow of a pre-geometric theory proposed by Wilczek. Its infrared limit exists, and corresponds to a fixed point where stochastic fluctuations vanish. Diffeomorphism symmetries are restored in this limit, where the theory is classical and expressed by the Einstein-Hilbert action. The infrared phase then corresponds to the classical theory of General Relativity, the quantization of which becomes meaningless. Away from the infrared limit, in the pre-geometric phase of the stochastic gradient flow, the relevant fields of the Wilczek theory undergo stochastic fluctuations. The theory can be quantized perturbatively, generating corrections to the classical Einstein-Hilbert action. The stochastic gradient flow also possesses an ultraviolet fixed point. The theory flows to a topological BF action, to which general non-perturbative quantization methods can be applied. Two phase transitions occur along the thermal time dynamics, being marked by: i) the breakdown of the topological BF symmetries in the ultraviolet regime, which originates the pre-geometric phase described by the Wilczek theory; ii) the breakdown of the parental symmetries characterizing the Wilczek theory, from which General Relativity emerges. The problem of quantizing the Einstein-Hilbert action of gravity finally becomes redundant.

Speaker: Prof. Antonino Marciano’ (Fudan University & INFN)

Marciano_Tartu2025.pdf

14:20 → 15:10 Sympy Workshop

Convener: Dr Laur Järv (University of Tartu)

General relativity (part 1).ipynb

Introduction to SymPy.pdf

15:10 → 15:15 Closing words

15:15 → 15:45 Goodbye Coffee