Schedule

I will briefly review metric-affine gravity stressing analogies to gauge theories of particle physics, then list some new examples of such theories that have healthy propagation on Minkowski space and finally give some new results concerning their renormalizability.

Postulated over a 100 years ago, General Relativity (GR) is the chief theoretical framework for gravity. However, an increasing number of formal considerations and experimental measurements strongly indicate that the theory is not complete. The ongoing search for a suitable extension of GR has led to a rich set of proposals, collectively known as Modified Gravity (MG). It is well-known that MGs generically suffer from instabilities that render the theories unphysical. Nevertheless, the interpretation, identification and correction of such prominent problem remain difficult and controversial tasks. In this talk, we will ponder over some of the most notable propositions in this regard.

The variational problem in general relativity is well-defined in spacetimes with boundaries only if we include a Gibbons-Hawking-York (GHY) boundary term to the total action. This is also true for extensions of general relativity, e.g. comprising of polynomials of the Riemann tensor. We go beyond general relativity and consider theories containing, in addition to curvature, arbitrary polynomials of torsion and non-metricity and consider the corresponding variational problem. In particular, in this talk I will present a new and efficient closed form expression for the Gibbons-Hawking-York (GHY) terms for theories of gravity with non-vanishing curvature, torsion and non-metricity. We find that only curvature dependent terms in the action contribute to the GHY term; Terms polynomial solely in torsion and non-metricity do not require any GHY term compensation for the variational problem to be well-defined. We test our method by confirming existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity. Moreover, we obtain new results for torsionful Lovelock-Chern-Simons and metric-affine gravity. Besides the explicit examples I will discuss in my talk, our formalism can be used to understand the boundary terms appearing in the geometrical trinity of gravity. For details, see Bastian Hess' contribution to this conference.

This talk is based on SciPost Phys. 14, 099 (2023).

We employ Ehlers transformations, Lie point symmetries of the Einstein field equations, to efficiently endorse accelerating metrics with a nontrivial NUT charge. Under this context, we begin by re-deriving the known C-metric NUT spacetime described by Chng, Mann, and Stelea in a straightforward manner, and in the new form of the solution introduced by Podolský and Vrátný. Next, we construct for the first time an accelerating NUT black hole dressed with a conformally coupled scalar field. These solutions belong to the general class of type I spacetimes, therefore cannot be obtained from any limit of the Plebanśki-Demiański family whatsoever and their integration needs to be carried out independently. Including Maxwell fields is certainly permitted, however, the use of Ehlers transformations is subtle and requires further modifications. Ehlers transformations do not only partially rotate the mass parameter such that its magnetic component appears, but also rotate the corresponding gauge fields. We present a Reissner-Nordström-C-metric NUT-like black hole that correctly reproduces the Reissner-Nordström-C-metric and Reissner-Nordström-NUT line elements in the corresponding limiting cases but with a misaligned electromagnetic potential.

I will re-derive the geometrical trinity of gravity which includes three dynamically equivalent theories: GR as well as its teleparallel (TEGR) and symmetric teleparallel (STEGR) equivalents in spacetimes with a boundary. In each step of the derivation, I will carefully add the necessary Gibbons-Hawking-York (GHY) terms. These terms need to be added to curvature based Lagrangians to make the variational problem well-defined. A generalized version for theories containing torsion and non-metricity in addition to curvature has been derived in arxiv:2211.02064, see the talk of Ioannis Matthaiakakis on this conference for details. Apart from carefully adding appropriate GHY terms, I will decompose the well-known boundary terms of TEGR and STEGR into boundary normal and tangent contributions. This decomposition reveals that the boundary terms of TEGR and STEGR equal differences of GHY terms. I will show that the well-posedness of the variational principle requires the elimination of all remaining boundary terms when taking the limit of vanishing curvature. In particular, this means that TEGR and STEGR do not require any boundary terms. In addition, I will discuss generalizations of the geometrical trinity of gravity to extensions of general relativity. This talk is based on arxiv:2304.06752.

Scalar hair of black holes in theories with a shift symmetry are constrained by no-hair theorems, with one of the most studied counterexamples being a linear coupling of the scalar with the Gauss-Bonnet invariant. I will present both theoretical and observational constraints on the presence of the scalar-Gauss-Bonnet operator. In particular, I will show that demanding that time advances are unobservable within the regime of validity of the effective field theory, its cutoff must be parametrically of the same size as the inverse Schwarzschild radius of the black holes for which the non-standard effects are of order one. For astrophysical black holes within the range of current gravitational wave detectors, this means a cutoff length of the order of kilometers.

In this talk, I will review the mathematical formalism leading to the 3+1 decomposition of the equations of motion of the teleparallel equivalent of general relativity in both Lagrangian and Hamiltonian formalisms. For this, I will assess the 3+1 decomposition of the tetrad field and its relation to the ADM decomposition of the metric and compare the resulting identities, constraints, and evolution equations. Also, I will present Hamilton's equations for the teleparallel equivalent and its pros and cons. Finally, I will discuss prospects for numerical relativity in the teleparallel framework.

Although we cannot understand the true nature of singularities in the framework of GR, it is possible to evade them by following a fairly simple strategy: generate regular BHs by filling the spacetime around the central singularity with some physically reasonable source of matter (which could be consequence of some new gravitational sector). This has produced a plethora of new regular BH solutions in recent years, mainly because the matter source used to evade the central singularity can be interpreted in terms of nonlinear electrodynamics. However, all these regular BH solutions contain a Cauchy horizon, a null hyper-surface beyond which predictability breaks down, and also leads to mass inflation at the perturbative level, a pathology which occurs even in loop quantum gravity inspired models. Even though the strong cosmic censorship conjecture establish the impossibility of extending spacetime beyond this region, in this talk we show how far we can go, without invoking this conjecture, in the building of a physically reasonable black hole without a Cauchy hyper-surface. Following this reasoning, we find a black hole lacking of Cauchy horizon, asymptotically flat and satisfying either the strong or dominant energy condition. The above is possible by demanding integrable singularity for the Ricci scalar, whose direct consequence is the appearance of finite tidal forces.

Remnant symmetries were discovered as a symmetry of a modified gravity model known as f(T) gravity. In this talk, I will show that remnant symmetries appear naturally and play an important role in teleparallel equivalent of general relativity as a symmetry related to the uniqueness of determination of the action. I will show some examples in the case of Minkowski, spherically symmetric and cosmological spacetimes. Then I will discuss some of their puzzling properties, particularly related to their non-group nature, and their relevance to understanding gravity.

We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz transformations, thus providing a full invariant characterisation of all the possible algebraic types of the torsion and nonmetricity field strength tensors in Weyl-Cartan space-times. As an application, we show that in the framework of Metric-Affine Gravity the field strength tensors of a dynamical torsion field cannot be doubly aligned with the principal null directions of the Riemannian Weyl tensor in scalar-flat stationary and axisymmetric space-times.

In this presentation we first discuss about several teleparallel geometries for some specific spacetimes. Then we present a complete perturbation theory suitable for teleparallel gravity. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation scheme can be transformed to one in which perturbations all take place within the co-frame. A covariant definition of a teleparallel Minkowski geometry is proposed. We compute the perturbed field equations for \(f(T)\) teleparallel gravity and discuss the stability of the teleparallel Minkowski geometry within \(f(T)\) teleparallel gravity.

In view of gaining insight regarding the nature of dark matter and dark energy, one can follow two distinct but complementary routes. On the one hand, one can try to modify Einstein's equations by adding new fields, providing a possible (effective) description of the unrated phenomenons while maintaining the assumptions related to the geometrical structure of spacetime. On the other hand, one can question the framework of pseudo-Riemannian geometry as being adapted to the full description of spacetime (typically, at cosmological scales). In the first case, scalar-tensor theories of gravity (and especially Horndeski gravity), where the new degrees of freedom are encoded by means of a scalar field(s), have been extensively investigated in the literature. This is especially true for the sector of Horndeski gravity including a non-minimal coupling of the scalar field to the Gauss-Bonnet invariant. In the later case, a minimal generalisation of GR's framework consist in relaxing the hypothesis linking the connection to the metric, leading to the framework of metric-affine gravity. This context reveals new starting points to generalise GR. In particular, on should mention the teleparallel equivalent to GR (TEGR). TEGR is formulated on a Weitzenbock space (where the linear connection exhibit only torsion) and has been interpreted as a reformulation of GR as a gauge theory of the translation group, bringing the formulation of gravity closer to the other fundamental interactions.

In this talk, I discuss the first explicit construction of asymptotically flat black holes endowed with scalar hair in a teleparallel generalisation of the sector of Horndeski gravity exhibiting non-minimal couplings to the Gauss-Bonnet invariant. This framework allows for more general couplings between the scalar field and the spacetime geometry that naturally encloses the couplings of Horndeski type. Our study includes, under the assumption of a static and spherically symmetric setup, the analytical construction of perturbed solutions around a Schwarzschild background and the explicit numerical construction of solutions of the full field equations. This reveals novel possible behaviors of the scalarized black holes as compared to the Horndeski case. In particular, non-monotonicity of the metric functions and the scalar field can appear, a feature that was not observed until now for static scalarized black hole solutions. Our study then provides an explicit demonstration of how scalar-torsion gravity (and possibly other non-Riemaniann models) provides a richer canvas for the study of phenomenology beyond GR and open the way for novel studies regarding scalarized black hole solutions in non-Riemannian theories of gravity.

This presentation is based on the work done in [arXiv:2212.07653 [gr-qc]] (https://arxiv.org/abs/2212.07653) in collaboration with Sebastian Bahamonde, Daniela Doneva, Christian Pfeifer and Stoytcho Yazadjiev.

Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Teleparallel gravity is based on the tetrad formalism. This turns out to result in a more general formalism of Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide range of models coming from ghost and Laplacian instabilities. The aim is to limit pathological branches of the theory by fundamental considerations. It is possible to conclude that a very large class of models results physically viable.

The generalization of the Rezzolla-Zhidenko theory-agnostic parametrization of black-hole spacetimes to accommodate spherically symmetric Lorentzian, traversable wormholes in an arbitrary metric theory of gravity is presented. The parametrization is similar in spirit to the post-Newtonian parametrized formalism, but with validity that extends beyond the weak field region and covers the whole space. The method is based on a continued-fraction expansion in terms of a compactified radial coordinate which leads to superior convergence properties and allows one to approximate a number of geometries in terms of a small number of coefficients. Calculations of shadows and quasinormal modes for various examples of parametrization of known wormhole metrics that we have performed show that, for most cases, the parametrization provides excellent accuracy already at the first order. Therefore, only a few parameters are dominant and important for finding potentially observable quantities in a wormhole background.

I will discuss an analog version of Horndeski gravity in a symmetric teleparallel geometry which assumes that both the curvature (general) and torsion are vanishing and gravity is only related to nonmetricity. The setup requires that the Euler-Lagrange equations for not only metric and scalar field but also connection should be at most 2nd order. The resulting theory can be recast as a sum of the Riemannian-Horndeski theory and new terms that are purely teleparallel. The nature of nonmetricity allows more possible ways of constructing 2nd-order theories of gravity than in the Riemannian case. In this regard, up to some assumptions, I will show the most general K-essence extension of symmetric teleparallel Horndeski gravity. I will also discuss a novel theory containing higher-order derivatives acting on nonmetricity while still respecting the 2nd-order conditions, which can be recast as an extension of Kinetic Gravity Braiding. Finally, I will present the FLRW cosmological equations for the model.

In this talk, we construct exact rotating wormholes through the employment of the Ehlers solution generation technique. This methodology is founded on the Ernst description of four-dimensional, stationary, and axially symmetric solutions of the Einstein-Maxwell theory. To commence, we adopt the static Barcelo-Visser wormhole derived from the Einstein-Maxwell-conformal-scalar theory as a seed, and demonstrate, through the Ernst approach, the feasibility of constructing two novel geometries of rotating wormholes. These geometries correspond to Barcelo-Visser wormholes embedded within rotating and magnetic backgrounds. The rotation in the first case is a result of the dragging effect of the rotating background on the initial static wormhole, while in the second case it is caused by the electromagnetic interaction between the charge of the static wormhole and the external magnetic field. We conduct a comprehensive analysis of the geometric properties of these configurations, and examine the new features introduced by rotation, such as the emergence of ergospheres. Recent evidence suggests that incorporating slow rotation can stabilise wormholes, rendering these exact, fully rotating solutions particularly appealing.

In this talk I will discuss what are to me the most promising future directions for teleparallel gravity. To give a sense of direction I will present some unsuccessful examples, in particular some constructions in teleparallel bigravity. However, the framework teleparallel bigravity provides promising constructions for investigate something known as partially masslessnes which admits a conformal symmetry removing the scalar mode of a massive spin 2 field. Another very interesting path is to investigate so called nontrivial tetrads, which is connected with a deeper understanding of Minkowski spacetime and the strong coupling problem.

Small perturbations of spherical symmetric Schwarzschild backgrounds in General Relativity have been already discussed since 1957 by Regge and Wheeler and the quasinormal frequencies of relativistic stars and black holes that emit gravitational waves have been investigated by Nollert [2], Kokkotas and Schmidt [3] as well since 1999. Considering the quite recent detection of gravitational waves in 2015 [4], it is interesting to go back to the topic of quasinormal modes. General Relativity -though a quite successful theory of gravity- is not able to address several issues like the nature of dark matter and dark energy and the accelerated expansion of the universe. Alternative theories of gravity appear to be better candidates and for this reason we will focus on the metric teleparallel theory in particular where the gravitational field is not mediated by the curvature as in GR but instead by the torsion. [5] We will discuss how we could approach the topic of quasinormal modes in this theory, following the recent master thesis work by Asuküla [5].

[1] T. Regge and J. A. Wheeler, "Stability of a Schwarzschild Singularity", Phys. Rev. 108, 1063–1069 (1957)

[2] K. D. Kokkotas and B. G. Schmidt, "Quasi-Normal Modes of Stars and Black Holes", Living Reviews in Relativity 2 (1999)

[3] H.-P. Nollert, "Quasinormal modes: the characteristic ’sound’ of black holes and neutron stars", Classical and Quantum Gravity 16, R159–R216 (1999)

[4] B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), "Observation of Gravitational Waves from a Binary Black Hole Merger", Phys. Rev. Lett. 116, 061102 (2016)

[5] K. Hayashi and T. Shirafuji, "New general relativity", Phys. Rev. D 19, 3524–3553 (1979)

[6] H. Asuküla, "Quasinormal modes of Schwarzschild black holes in 1-parameter New General Relativity" (2021) (Master Thesis, Institute of Physics, University of Tartu)

I will discuss some work in Palatini theories, where the connection is an independent degree of freedom. I will comment on inflation, which is an interesting arena for Palatini, the stability if various theories, and the extension of the Palatini formulation to particle physics gauge theories.

Geometrical methods of quantum mechanics make it possible to extend the classical phase space by quantum degrees of freedom. Using recent progress in explicit derivations of the phase space structure of states for two degrees of freedom, it is shown that a quantum test mass in a correlated or impure state experiences proper time derived from a Finslerian extension of Minkowski space-time.

A Comprehensive dynamical system analysis of Cosmological Models at background and perturbation levels

Dynamical systems techniques are valuable tools to study a cosmological model's complete qualitative dynamical behaviour without analytically solving the highly non-linear set of differential equations. Usually, we apply the dynamical system approach at the background level. However, we can also apply the analysis at the perturbation level. Hence, with this combined analysis, we can determine both the background stable late-time solutions and the growth of the structure formation, independent of the specific initial conditions. Further, Singular and Bifurcation analyses can complement the dynamical system analysis. In this talk, I will give an overview of how various tools of dynamical systems techniqes can be used in analysing cosmological context. Finally, I will discuss a specific scenario where through the independent approach of dynamical systems, we verify the observational confrontation results, namely that \(f(Q)\) gravity can be considered an up-and-coming alternative to the \(\Lambda\)CDM concordance model.

I will present a new family of exact vacuum solutions to Pfeifer and Wohlfarth's field equation in Finsler gravity, consisting of Finsler metrics that are Landsbergian but not Berwaldian, also known as unicorns due to their rarity. These solutions have a physically viable light cone structure, even though in some cases the signature is not Lorentzian but positive definite. Furthermore there exists a promising analogy between the solutions and classical FLRW cosmology. One of the solutions in particular has cosmological symmetry, i.e. it is spatially homogeneous and isotropic, and it is additionally conformally flat, with conformal factor depending only on the timelike coordinate. This conformal factor can be interpreted as the scale factor and corresponds to a linearly expanding (or contracting) Finsler universe.

We study the global phase portraits of singe scalar field inflation models nonminimally coupled to gravity in the metric and Palatini formalisms, and investigate the following. Does the qualitative picture that inflation is ruled by a heteroclinic orbit in the phase space generally hold? Does the qualitative picture that most solutions start in a kinetic regime from a fixed point in the asymptotics still hold? In the cases when the metric and Palatini models predict the same values for observables in the slow roll approximation, are the phase portraits also indentical? What about the range of initial conditions that can give more than 50 e-folds of accelerated expansion? How good is the slow roll approximation in relation to the actual inflationary trajectory?

Berwald spacetimes are Finsler spacetimes which are closest to Riemannian (GR) ones, in the sense that they canonically define a symmetric affine connection on the spacetime manifold. In the paper, we first locally classify all SO(3)-invariant 4-dimensional Berwald-Finsler structures and then use the obtained solutions as ansatzes in a Finslerian generalization of the vacuum Einstein field equations. In particular, we determine all spatially spherically symmetric, asymptotically flat and stationary, respectively, static Berwald-type vacuum solutions. (joint work with S. Cheraghchi and C. Pfeifer)

General relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine gravity, which avoids any assumption about the vanishing of curvature, torsion, or nonmetricity. We use it to construct an action of a scalar field coupled nonminimally to gravity. It encompasses as special cases numerous previously studied models. Eliminating nonpropagating degrees of freedom, we derive an equivalent theory in the metric formulation of GR. Finally, we give a brief outlook of implications for Higgs inflation.

If the spacetime geometry is given by a Finsler metric of Lorentzian signature, rather than by a pseudo-Riemannian metric, Maxwell's equations can be formulated in two different ways: Either one has to allow the electromagnetic field strength to depend not only on the spacetime coordinates but also on the velocity coordinates, or one has to make Maxwell's equations into pseudo-differential equations. Here I will argue in favour of the second possibility, and I will discuss some of the consequences. Among other things, I will demonstrate that the high-frequency limit (geometric-optics approximation) is well defined and that it leads to the conclusion that light rays are lightlike Finsler geodesics.

We explore the stability of theories where the action has arbitrary algebraic dependence on Ricci-type tensors: the three first traces of the Riemann tensor. We consider the case where the connection is unconstrained and the cases where either non-metricity or torsion is assumed to vanish. We show which combinations of the Ricci-type tensors lead to new degrees of freedom around Minkowski and FLRW backgrounds, and whether they are stable or not. Then, we will investigate how the higher order terms can affect inflation. We do this in a model where the action has arbitrary algebraic dependence on the symmetric part of the Ricci tensor.

The Hamiltonian constraint of general relativity is often described as a fundamental problem for theories of quantum gravity and our usual understanding of dynamics therein: As time does not explicitly appear, theories of quantum gravity have to face the so-called “problem of time”. In recent years, older attempts of resolving this tension through relational dynamics, for example, the Page-Wootters formalism, have seen a resurgence and received a lot of attention, culminating in a more unified understanding of different approaches. Classically, time-travel is ruled out (or at the very least contra-indicated) for a long list of reasons. Nevertheless, it often rears its head when assumptions of general relativity have to be relaxed, and it can often provide for tests and new perspectives on better-behaved physics. In this project, we attempt to answer what happens when an emergent notion of time in a quantum system meets the concept of time travel. We study what this can tell us as to how to even define time travel with only relational dynamics, and what new or improved limitations can be formulated through this point of view.

In this talk, we will discuss about the Higgs vacuum decay. The measured masses of the top quark and Higgs boson support the notion that the Higgs potential becomes unstable at high field values, leading to a potential decay. We explore the scenario where the Higgs boson is non-minimally coupled to both the Ricci scalar and the Holst invariant in the context of metric-affine gravity. Our findings indicate that this framework significantly enhances the vacuum stability over a broad range of model parameters.

The C-metric represents the spacetime of a pair of black holes undergoing uniform acceleration. The acceleration mechanism is physically represented by a cosmic strings of which its mathematical trace on the metric is given by a conical defect. In this talk we propose to construct three-dimensional accelerating black holes in anti de Sitter, and to study their geometric and thermodynamic features from an AdS/CFT perspective. In addition, we will also show how these geometries can accept the presence of scalar hair.

We propose an extension of the Higgs inflation to the hybrid metric-Palatini gravity, where we introduce non-minimal couplings between Higgs and both the metric-type and the Palatini-type Ricci scalars. As the ultraviolet (UV) cutoff as a low-energy effective field theory (EFT) of this model is significantly lower than the Planck scale due to a strong curvature of field-space, we consider a possible candidate of UV-extended theories with an additional scalar field introduced so as to flatten the field-space in five-dimension. While the field-space can be flatten completely and this approach can lead to a weakly-coupled EFT, we gain an implication that Planck-scale EFT can be only realized in the limit of metric-Higgs inflation.

We propose a functional measure over the torsion tensor. We discuss two completely equivalent choices for the Wheeler-DeWitt supermetric for this field, the first one being based on its algebraic decomposition, the other inspired by teleparallel theories of gravity. The measure is formally defined by requiring the normalization of the Gaussian integral. To achieve such a result we split the torsion tensor into its spin-parity eigenstates by constructing a new, York-like, decomposition. Of course, such a decomposition has a wider range of applicability to any kind of tensor sharing the symmetries of the torsion. As a result of this procedure a functional Jacobian naturally arises, whose formal expression is given exactly in the phenomenologically interesting limit of maximally symmetric spaces. We also discuss the explicit computation of this Jacobian in the case of a 4-dimensional sphere, which is the Euclidian counterpart of de Sitter space, writing its logarithmic divergences.

We study the generation of primordial magnetic fields and EW hypermagnetic fields in the Einstain-Cartan portal with gauge bosons. The estimates obtained for \(B_{W}\) are similar to the one obtained from the ferromagnetic models obtained before by et al (Phys Lett B (1998)). The main difference is that the value of weak boson squared mass is multiplied by an amplification factor which depends upon the torsion scalar. Torsion data from LHC torsion is used (Almeida, Nepomuceno et al PRD (2017)). Einstein-Cartan-Holst gravity equations are also discussed in the famework of hyper.dynamo

We consider a generic action quadratic in the torsion field coupled to a Riemannian background. We study the logarithmic divergences arising in four dimensions for such a theory and analyze its UV behavior. The computation is heavily based on covariant methods like the covariant Seeley-DeWitt expansion of the heat kernel and the covariant spin-parity decomposition of the torsion.

How can we look at the huge landscape of proposed theories of gravity without getting lost? We live in a very flourished moment for cosmological data and now more than ever is fundamental to look for criteria to organize the uncountable number of proposed theories. What we know is that general relativity is not the end of the story. Many proposals go towards adding to general relativity some unknown elements to explain observations. These are dark energy and dark matter. The candidates to explain these unknown are many and by now the main actor is the \(\Lambda\)CDM model. On the other hand, many proposed theories choose to modify the very same geometrical description given by general relativity. This way of proceeding tries to substitute or complement the introduction of uknown elements. To proceed in this jungle of proposals we neeed to choose some criteria because we want to focus on the fact that experiments test principles and not specific theories. The criteria that we choose are the equivalence principles, the cosmological principle and the distance duality relation. Each of these tools is based on some set of theoretical assumptions and can be connected to some observable quantities. The combined use of these criteria can help us looking to cosmological data to find a good candidate to be our gravitational theory. We can start analysing these criteria for some specific theories. One first example can be a model with non minimal coupling between a scalar field and matter. Another interesting example can be theories with torsion. The theoretical assumptions behind the three chosen criteria may be various enough to explore a good amount of theories of gravity.

In the present work, we study the dynamics of a general null hypersurface in the Einstein Cartan (EC) theory generated by a null vector field \(l^a\). We see that under a particular relation between the torsion tensor and the null generators called the geodesic constraint, the dynamical evolution of the Hajicek one-form is governed by the component \(\hat{G}_{ab}l^a q^b_{~c}\), where \(q_{ab}\) is the induced metric on an orthogonal spacelike cross-section of the null surface and \(\hat{G}_{ab}\) is the analogue of the Einstein tensor in spacetime with intrinsic torsion. Using the gravitational field equations for the EC theory, we see that above mentioned evolution equations can be provided a fluid-dynamical interpretation respectively. The relevant fluid parameters have been properly identified. The dynamics of the Hajicek one-form has been studied in a local inertial frame and its correspondence with Cosserat fluid has been established. The presentatation will be mainly based on Phys. Rev. D 106, 104005 (2022)and Phys. Rev. D 105, 064047 (2022).

In this talk, we will show that metric-Palatini gravity, extended with the antisymmetric part of the affine Ricci tensor and extended also with a matter sector involving the affine connection, reduces dynamically to general relativity plus a geometric massive vector field such that the geometric vector couples to fermions in a universal fashion. We show that due to its geometrical origin this geometric vector, the geometric Z′, does not couple to scalars and vector bosons. It couples only and only to fermions in a universal fashion. We show that this geometric Z′ could well be a viable dark matter candidate. We also show that this geometric Z′ hampers black hole formation, and its matter couplings worsens the situation. We will briefly discuss the possible black hole solutions in the Einstein-geometric Proca model in the AdS background. We close the talk with future prospects concerning collider, black hole and other consequences of the geometric Z′.

Gravitational waves are among the ultimate tools to test fundamental physics and promise to answer the long-waiting question about the nature of gravity in the regime of strong fields. The degeneracies between different effects are a serious obstacle, though, to fulfilling this goal since modified gravity often leads to smaller cumulative changes. In the present talk, we will focus on an interesting new effect that differs qualitatively from the standard picture in general relativity. These are the gravitational phase transitions during which a compact object like a black hole or a neutron star can completely emit or acquire new scalar hair through a process resembling a first-order matter phase transition. Such an effect is present in a number of modified theories of gravity and provides interesting smoking gun effects beyond-GR that can be easily traced in observations.

In his seminal paper, Bianchi gave a classification of three-dimensional Riemannian manifolds which admit a transitive group action, under which the metric is invariant, and identified 9 types of spaces, depending on the Lie algebra structure of the translation generators. Considering these spaces as spatial equal-time slices of a four-dimensional spacetime, these so-called Bianchi types also give rise to different classes of spatially homogeneous metrics, with the spatially homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker metric as a particular example. The same group actions can also be applied to teleparallel and metric-affine geometries, where either a tetrad and a spin connection, or an additional, possibly flat affine connection appears as the fundamental field variable. In my presentation I give an insight to the construction of the most general homogeneous teleparallel and metric-affine spacetimes and their application to gravity theory.

I will illustrate how gravity impacts the properties of stellar objects and emphasize the significance of incorporating a realistic description to effectively constrain theories. Additionally, I will provide a brief discussion on the effective Poisson equation derived from non-commutative geometry and compare it to the modified gravity results.

We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid.The latter is a generalization of the usual Perfect Fluid notion that includes also a non-vanishing hypermomentum tensor that is compatible with the Cosmological Principle and encodes the microscopic characteristics of matter. Then, the equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of torsion and non-metricity vectors. In this setup, studying the modified Friedmann equations along with the conservation laws of the perfect cosmological hyperfluid, we provide exact solutions both for purely dilation and for purely spin hypermomentum sources. We then discuss the physical consequences of our model and the prominent role of torsion and non-metricity in this cosmological setup.

The standard theory of star evolution fails to explain various aspects of stellar structure. This study aims to address this limitation by reexamining stellar theory through the lens of Modified Gravity. Specifically, we apply the weak field limit to f(Q) theories, deriving the modified Poisson equation. We explore different forms of the f(Q) functions and their impact on the Poisson equation. Additionally, we investigate modifications to the hydrostatic equilibrium equation and the Lane-Emden equation, along with their practical applications.

In symmetric teleparallel geometry the curvature and torsion tensors are assumed to vanish identically, while the dynamics of gravity is encoded by the nonmetricity. Here the spatially homogeneous and isotropic connections that can accompany flat Friedmann-Lemaitre-Robertson-Walker metric come in three sets. As the trivial set has received much attention, in this work we focus upon the two alternative sets which lack a Minkowski limit. Working in the context of symmetric teleparallel scalar-tensor gravity with generic coupling functions, we show that the extra free function in the connection can not play the role of dark matter nor dark energy. We study under which conditions these cosmological spacetime configurations with radiation and dust matter content relax to the limit of general relativity.

We present the Tolman-Oppenheimer-Volkoff (TOV) equation for stellar structure in equilibrium in the scalar-tensor version of symmetric teleparallel gravity. This theory is constructed with vanishing curvature and torsion, but nonzero non-metricity tensor. We demonstrate the derivation and result for the TOV equation as well as further interesting processes that can be analised from this starting point.

Albeit all being bosonic theories, unification of gauge theory and gravity has eluded full success thus far. There is similarity to be found in every approach, from the metric action of Einstein-Hilbert, to Plebanski theory, TEGR and STEGR, or Ashtekar's variables, to Loop Quantum Gravity, and in many others. To approach this from the other side, the Yang-Mills gauge theory of fundamental interactions itself could be pushed towards a form more suggestive of gravitation. In particular, when lowering Yang-Mills theory to first order, the likeness with Palatini gravity is evident, yet the constructions do not appear to be extensively studied. Ever modifying and adapting the first order theories, new phenomenology can be found, new extensions to be studied, a different perspective into unification to be looked into; which the presentation hopes to be informative of. Yet it will still remain to be seen whether the similarity is superficial, or deeper.

Compact stars with Kaluza-Klein excitations are considered and constraints on the size of compactified extra dimensions are given.

The model is a static, spherically symmetric Kaluza-Klein-based theory with one extra compactified dimension. Realistic equation of state has been introduced and applied in order to reproduce the compact star observables. Comparison of the theoretical calculation with available observational data led us to consequences on the size of extra dimensions within the Kaluza-Klein framework.

In this talk, we will explore the Stueckelberg procedure and how to apply it to General Relativity and Unimodular Gravity in order to get a new theory with an enhanced symmetry containing them both. In this setting, we realize that Stueckelberg-ing one of them and then gauge fixing to the other one is not consistent. Such restriction cannot be achieved in a continuous way, i.e., with a legal gauge fixing, as a consequence of the global degree of freedom that is exclusively present in Unimodular Gravity.

I will discuss the process of gravitational collapse in pure Gauss-Bonnet gravity. In the homogeneous dust collapse, I will show that in the marginally bound case, the \(D=7\) pure Gauss-Bonnet theory has indistinguishable gravitational dynamics with Einstein's theory in \(D=4\). In D>7 pure Gauss-Bonnet gravity becomes weaker, while in D<7 it becomes stronger. This is not the case in the bound/unbound collapse, where pure Gauss-Bonnet is always weaker/stronger than general relativity. I will also present the inhomogeneous dust collapse and specifically the critical mass modes in different dimensions, for which both naked singularities and black holes can occur.

We present a model of gravity where the Lagrangian has a dependency on the action. This leads to new terms in the field equations, which cannot be easily obtained with the usual approaches. Action-dependent theories are based on the Herglotz variational principle, which is intricate for field theories. We explain recent theoretical results and the consequences for General Relativity. The dependence on the action usually leads to non-conservative behavior, although for field theories the phenomenology is much richer. In this regard, we will show new applications to cosmology.

The study of junction conditions is of paramount importance in the context of gravitational theories. Physically-relevant scenarios in which two solutions are separated by a boundary layer are ubiquitous, with stars surrounded by vacuum or the so-called thin-shell wormholes being paradigmatic examples. In this talk, we will present the junction conditions in the ghost-free subclass of quadratic Poincaré Gauge Gravity. We will show that, in this theory, the matching interface is allowed to host surface spin densities, as well as energy-momentum thin shells and double layers. We shall also discuss the relevance of our results and their practical applications.

Since the first detection by Advanced LIGO of a black hole binary merger, about 90 compact object coalescences have been observed by the LIGO–Virgo–KAGRA collaboration, allowing us to test astrophysical models of compact objects, early universe processes, beyond the Standard Model particle physics, and theories of classical or even quantum gravity. I will first present constraints on astrophysical/cosmological models from the non-detectability of the gravitational-wave background and then highlight implications from the detected transient gravitational waves.

I will discuss the emergence of the Carrollian (c->0) limit in the holographic description of asymptotically flat geometries. Some possible consequence and research directions will be reviewed.

In this work we describe metric-affine theories anew by making a change of field variables. A series of equivalent frameworks is presented and identifications are worked out in detail. The advantage of applying the new frameworks is that any MAG theory can be handled as a Riemannian theory with additional fields. We study the Hilbert-Palatini action using the new field variables and disclose interesting symmetries under SOSO transformations in field space. Then, we use certain Riemannian theories as seed models for MAG theories, restricting ourselves to three examples. We present a black hole solution with torsion and non-metricity which under a certain tuning acquires a regular core. A de Sitter universe with the expansion powered by 3-form torsion, is also reported.

In this work we build the general formalism of gravitational lensing in luminal Horndeski models, deriving the Jacobi matrix equation and the general angular diameter distance in Horndeski theories through the screen space formalism. We generalize the focusing and multiple lensing theorems to include Scalar Tensor theories belonging to the luminal Horndeski class and derive constraints they must satisfy to exhibit the same gravitional lensing behavior in General Relativity. This provides a way to test theories through Strong Lensing effects, as well as a full theoretical framework for testing lensing in these theories. We find that for some theories, like metric f (R) and unified k-essence, the conditions are satisified in general physical cases, while for others like Galileon Condensate models, the conditions impose constraints on the parameter space of the theory.

We present a computer algebra package for computing the particle spectrum of any linearised metric-affine gravity (MAG) theory. Any parity-preserving scalar Lagrangian quadratic in the metric and the general rank-three connection is accepted as input. The package is based on the usual spin-projection operator formalism, which separates the particle interactions among sectors of a given spin and parity. The kernel of the wave operator matrix is automatically translated into (covariantly expressed) constraints on the hyperfluid source currents. The saturated propagator is then formed from the pseudo-inverse. Massive poles and their residues are identified, along with their no-ghost/no-tachyon conditions. For the massless sector, the constrained sources are expressed component-wise on the null cone and their eigenvalues computed. The package is parallelised for use on desktop computers or clusters/supercomputers. Future work promises automated, recursive searches over the wave operator determinant root system, aiming to exhaustively list all (linearly) viable critical cases of the MAG. In the shorter term, the package facilitates the study of MAG theories in which torsion and nonmetricity are simultaneously present: it has previously been more usual to (kinematically) disable one of these fields for each analysis. Finally, we discuss the role of accidental (linear-only) symmetries in the MAG.

Recent astrophysical observations by the GRAVITY collaboration and the EHT have suggested the existence of black-hole-like objects in the universe. However, black-hole spacetimes are problematic from a mathematical and physical point of view. To overcome this limitation, several alternative compact objects have been proposed, including perfect fluid stars, bosonic stars, Proca stars, fermionic stars, and wormholes. In this talk, we explore the validity of these alternatives by simulating the observational properties of accretion disks and isotropically emitting sources orbiting a central exotic compact object. Specifically, we investigate whether these alternative objects can replicate the observational properties of black-hole spacetimes, namely if they could cast a shadow and how their astrometric properties, e.g. the magnitude and centroid of the observation, compare with the black-hole scenario.

In this talk, I will present the computation of conformally covariant actions and operators for tensors with mixed symmetries in arbitrary dimension d. For the present case, tensors with mixed-symmetries arise because a general GL(d) connection depends on a three-indexed tensor, which is enough to contain the first two nontrivial mixed-symmetric irreducible representations, known as the traceless hook-symmetric and hook-antisymmetric tensors. The results I will show complete the classification of conformal actions that are quadratic on arbitrary tensors with three indices, which allows to write corresponding conformal actions for all tensor species that appear in the decomposition of the distorsion tensor of an arbitrary metric- affine theory of gravity including both torsion and nonmetricity. I will also discuss the degrees of freedom that such theories are propagating, as well as interacting metric-affine theories that enjoy the conformal actions in the Gaussian limit.

With the increasing precision of instruments detecting phenomena close to the event horizon of black holes (BHs), the possibility of new visual signatures can be investigated, testing the evidence for BH mimickers. In this work, we analyze the visual properties of infra-red radiation sources e.g. hot spots around relativistic constant density fluid stars supported by a thin shell. We consider configurations of the fluid star without a thin shell, with and without light rings (LRs). With a supplementary analysis focused on finding the radii of LRs for various configurations, we produce astrometric data via simulations in the GYOTO software. Our results imply qualitative differences in the visual signatures of the hot spot – we find configurations, which resemble either classic BHs, non-ultra compact horizonless compact objects or ultra-compact horizonless objects. Thus, we have found observational properties, which validate the fluid star model as a BH mimicker, as well as qualitative differences, which could be used to distinguish the compact object from a classic BH. By the next generation of experiments in gravitational physics, this distinction might become possible.

In this talk I will present sufficient conditions for the appearance of singularities in gravitational theories which propagate an extra vector degree of freedom, based on the known relaxations of the singularity theorems. I will also show specific cases of singular behaviours that usually would be considered as potentially singularity-free, since they violate the usual point-like energy conditions.

There is reason to believe that some gravitational wave signals detected in the near future are gravitationally lensed. The effect of this lensing is to magnify the signal. This amplification of the signals and the production of multiple signals from the same source separated in time opens up new scientific frontiers such as precision cosmology studies, detection of stellar-mass objects and intermediate-mass black holes, tests of the speed of gravitational waves etc. Additionally, it also opens up a new way to test and set constraints on different theories of gravity. In this presentation, we compare Palatini f(R) theory of gravity with General Relativity - in certain selected aspects - and also on the basis of selected examples. We use the eikonal approximation to study the geometric-optical limit of lensing and derive the evolution of gravitational waves. Furthermore, for the Singular Isothermal Sphere, we compute the Kirchhof diffraction integral and show that amplification factor shows deviations from the corresponding results in General Relativity.

It is a well-known fact that there is no well-defined notion of energy in gravity. In my opinion, it is not a big deal. Energy is a rather aritificial quantity which works perfectly as long as we have a natural symmetry with respect to translations in time, however not when there ceases to be any notion of an objective time, rather than a mere coordinate. However, recently we've got an essential progress in teleparallel models of gravity, with emerging opinions of having solved the "problem of energy". I will explain why I think it simply makes no good sense to go for "solving" a non-existent problem, and the correct answer is just that in general there is no such thing as The Energy.

Primordial black holes (PBHs) forming out of the collapse of enhanced cosmological perturbations provide access to the early Universe through their associated observational signatures. In particular, enhanced cosmological perturbations collapsing to form PBHs are responsible for the generation of a stochastic gravitational-wave background (SGWB) induced by second-order gravitational interactions, usually called scalar induced gravitational waves (SIGWs). This SGWB is sensitive to the underlying gravitational theory, therefore it can be used as a novel tool to test the standard paradigm of gravity and constrain possible deviations from general relativity. In this talk, I will analyse the aforementioned GW signal within modified teleparallel gravity theories by developing a formalism for the derivation of the GW spectral abundance within any form of gravitational action. Concrete results will also be presented for specific models of modified teleparallel theories.

The state of art in gravity theory is reviewed. New applications include black holes and cosmology.

A non-vanishing dark matter's spin tensor could be a source of torsion on cosmological scales. We analyze how this torsion generally creates anomalous propagation of GW polarization, and put some constraints on measurement possibilities.