Cartan geometry and gravitation (Invited talks)

• Thomas Zlosnik (University of Gdansk)

Room: A106 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.

Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality (Invited talks)

• Salvatore Capozziello (INFN - National Institute for Nuclear Physics)

Room: A106 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.

Self-excited instantons and the non-trivial structure of the teleparallel vacuum (Contributed talks)

• Martin Krssak (Comenius University in Bratislava)

Room: A106 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.

Finsler Geometry and the Fabric of Spacetime

• Nicoleta Voicu (UniTBV)

Room: A106 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.

Bounding anisotropic Lorentz Invariance Violation (Contributed talks)

• Merce Guerrero (University of Aveiro)

Room: A106 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 $c^{(6)}_{(I)jm}$.

Weak equivalence principle and nonrelativistic limit of general dispersion relations (Contributed talks)

• Christian Pfeifer (University of Bremen, ZARM)

Room: A106 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.

Finsler geometry as a window to Planck scale physics (Contributed talks)

• Iarley Lobo (Federal University of Lavras)

Room: A106 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.

From stars and seismic waves to the fundamentals of gravity

• Aneta Wojnar (Tartu University)

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.

Joining black hole imaging and ringdown: A novel view of testing gravity (Invited talks)

• Che-Yu Chen (iTHEMS, RIKEN)

Room: A106 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.

No vacuum? No problem! (Contributed talks)

• Verónica Errasti Díez

Room: A106 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.

Imaging black holes and horizonless compact objects (Contributed talks)

• Diego Rubiera-Garcia (Complutense University of Madrid)

Room: A106 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.

Gravitational wave propagation in hybrid metric-Palatini gravity (Contributed talks)

• João Luís

Room: A106 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.

4D GR via triples of 2-forms

• Kirill Krasnov (University of Nottingham)

Room: A106 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.

On the Gravitational Foundations of Geometry (Contributed talks)

• Tomi Koivisto (University of Tartu)

Room: A106 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.)*

Removing spurious degrees of freedom from EFT of gravity (Invited talks)

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

Room: A106 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.

Primordial Black Holes, Extremality, and Dark Matter: Rethinking Evaporation Limits (Contributed talks)

• Sebastian Schuster (Stockholm University)

Room: A106 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.

Quasinormal modes and absorption cross-section of a Bardeen black hole in presence of perfect fluid dark matter (Contributed talks)

• ANGEL RINCON RIVERO (Universidad de Alicante)

Room: A106 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.

Black holes and naked singularities in four dimensional dS and AdS Chamseddine gravity (Contributed talks)

• Branislav Cvetković (Institute of physics, Belgrade)

Room: A106 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.

Introducing Cadabra, a field-theory motivated approach to symbolic computer algebra (Invited talks)

• Kasper Peeters (Durham University)

Room: A106 The [Cadabra symbolic computer algebra system][1] 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. [1]: https://cadabra.science/

Emergent Gravity from Topological Quantum Field Theory: Stochastic Gradient Flow Perspective away from the Quantum Gravity Problem (Invited talks)

• Antonino Marciano’ (Fudan University & INFN)

Room: A106 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.