Schedule

I will present an overview of several recent works on Ricci-Based Gravity theories (RBGs). We will see how the dynamics of these theories can be studied from within GR itself and then will provide some examples of applications involving scalar fields, fluids, and electromagnetic fields. In particular, I will discuss the properties of some exotic scalar compact objects, boson stars, rotating charged objects, and multicenter solutions. I will also comment on experimental constraints on these theories.

We discuss black hole solutions in the Yang-Mills type models of the Poincare gauge gravity theory.

In this work we derived exact gravitational wave solutions in a general class of quadratic metric-affine gauge gravity models. The Lagrangian includes all possible (even-parity) linear and quadratic invariants constructed from the torsion, nonmetricity and the curvature. The ansatz for the gravitational wave configuration and the properties of the wave solutions are patterned following the corresponding ansatz and the properties of the plane-fronted electromagnetic wave.

We construct slowly rotating vacuum configurations endowed with both dynamical torsion and nonmetricity fields in the framework of Metric-Affine gauge theory of gravity. For this task, we consider scalar-flat Weyl-Cartan geometries and obtain under the slow rotation approximation an axisymmetric Kerr-Newman solution in the decoupling limit between the orbital and the spin angular momentum.

We study exact solutions of infinite derivative gravity within the class of so-called almost universal spacetimes. For such an ansatz, the field equations reduce to a single non-local but linear equation which is exactly solvable with the ghost-free choice \(\exp(-\ell^2 \Box)\) of the non-local form factor by eigenfunction expansion or using the heat kernel method. This procedure allows us to obtain non-local analogues of Aichelburg–Sexl and Hotta–Tanaka solutions which represent gravitational waves generated by null sources propagating in Minkowski, de Sitter or anti-de Sitter backgrounds. We discuss properties of these non-local solutions and also point out that the non-locality regularizes curvature singularities at the locations of the sources.

The observation of GW170817 binary neutron star (BNS) merger event has imposed strong bounds on the speed of gravitational waves (GWs) locally, inferring that the speed of GWs propagation is equal to the speed of light. Current GW detectors in operation will not be able to observe BNS merger to long cosmological distance, where possible cosmo- logical corrections on the cosmic expansion history are expected to play an important role, specially for investigating possible deviations from general relativity. Future GW detectors designer projects will be able to detect many coalescences of BNS at high z, such as the third generation of the ground GW detector called Einstein Telescope (ET) and the space-based detector deci-hertz interferometer gravitational wave observatory (DECIGO). In this paper, we relax the condition cT /c = 1 to investigate modified GW propagation where the speed of GWs propagation is not necessarily equal to the speed of light. Also, we consider the possibility for the running of the Planck mass corrections on modified GW propagation. We parametrize both corrections in terms of an effective GW luminosity distance and we per- form a forecast analysis using standard siren events from BNS mergers, within the sensitivity predicted for the ET and DECIGO. We find at high z very strong forecast bounds on the running of the Planck mass, namely O(10^{−1}) and O(10^{−2}) from ET and DECIGO, respec- tively. Possible anomalies on GW propagation are bound to |cT /c − 1| ≤ 10^{−2} (10^{−2}) from ET (DECIGO), respectively. We finally discuss the consequences of our results on modified gravity phenomenology.

We study the relation between quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope. With the help of WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and shadow radius of the same black hole. Some examples fulfilling the correspondence are provided.

This talk will be related to show the main classical gravitational tests for a recently found vacuum solution with spin and dilation charges in the framework of Metric-Affine gauge theory of gravity. Using the results of the perihelion precession of the star S2 by the GRAVITY collaboration and the gravitational redshift of Sirius B white dwarf we constrain the corrections provided by the torsion and nonmetricity fields for these effects

The phenomena of standing waves is well known in mechanical and electromagnetic setting where the wave has the maximum and minimum amplitude at the antinodes and nodes, respectively. In context of exact solution to Einstein Field equations, we analyze a spacetime which represents standing gravitational waves in an expanding Universe. The study the motion of free masses subject to the influence of standing gravitational waves in the polarized Gowdy cosmology with a three-torus topology. We show that antinodes attract freely falling particles and we trace the velocity memory effect.

We present a class of Horndeski scalar-tensor theories derived from a dimensional regularization of the critical (\(d=2p\)) Lovelock theories. This generalizes many recent results focused on the four-dimensional regularization of Gauss-Bonnet gravity. It is shown that these theories constitute a natural extension of Lovelock gravity at and above the critical order, because they reduce to Lovelock-like systems in \((d=2+n)\) warped geometries with maximally symmetric horizons. New non-Lovelock odd-dimensional black holes are also found to have a constant metric potential at the origin, although still singular there.

The lack of rotating black hole models, which are typically found in nature, in loop quantum gravity (LQG) substantially hinders the progress of testing LQG from observations. Starting with a non-rotating LQG black hole as a seed metric, we construct a rotating spacetime using the revised Newman-Janis algorithm. The rotating solution is non-singular everywhere and it reduces to the Kerr black hole asymptotically. In different regions of the parameter space, the solution describes i) a wormhole without event horizon (which, we show, is almost ruled out by observations), ii) a black hole with a spacelike transition surface inside the event horizon, or iii) a black hole with a timelike transition region inside the inner horizon. It is shown how fundamental parameters of LQG can be constrained by the observational implications of the shadow cast by this object. The causal structure of our solution depends crucially only on the spacelike transition surface of the non-rotating seed metric, while being agnostic about specific details of the latter, and therefore captures universal features of an effective rotating, non-singular black hole in LQG.

Investigation of exact solutions of anisotropic homogeneous cosmological models, the Bianchi-I type being the simplest of them, in modified gravity theories helps to discover new physical properties of these theories not seen in their FLRW solutions. In this talk, I consider two examples of such theories: the generic Horndeski family of models and the cubic gravity. In the first case, it has been investigated in which Horndeski models anisotropy grows with the spatial volume contraction similar to GR, and in which it is damped [1] (the effect first found in some specific Horndeski models in [2]). In the second case, it is shown that a specific metric cubic gravity which FLRW solutions do not have ghosts does contain a ghost degree of freedom in Bianchi-I type solutions as expected [3].

1. R. Galeev, R. Muharlyamov, A. A. Starobinsky, S. V. Sushkov, M. S. Volkov. Phys. Rev. D 103, 104015 (2021); arXiv:2102.10981.
2. A. A. Starobinsky, S. V. Sushkov, M. S. Volkov. Phys. Rev. D 101, 064039 (2020); arXiv:1912.12320.
3. M. C. Pookkillath, A. De Felice, A. A. Starobinsky. J. Cosm. Astropart. Phys. 2007 041 (2020); arXiv:2004.03912 [gr-qc].

I will discuss how spontaneous symmetry breaking of scale symmetry leads to dilaton decoupling in a scale invariant universe. This decoupling manifests itself in (at least) three different regimes: the absence of fifth forces, the non-mixing of adiabatic and isocurvature modes in inflation and the existence a massless, breathing mode in the quasi-normal modes of black hole ringdown.

\(f(R)\) is one of the very well studied classes of modified gravity theories for cosmology. Nonlinearities in the field equations compel us to take the resort to dynamical systems approach while studying cosmology in \(f(R)\) gravity. All the existing dynamical systems formulation for cosmology in \(f(R)\) gravity requires one to know a-priori the specific functional form of \(f(R)\) to make the system autonomous. In my presentation, I will introduce a new dynamical system formulation for cosmology in \(f(R)\) gravity that we recently proposed (2103.02274), which is free from this limitation. The trick is to expand the phase space by including the cosmographic parameters in the set of dimensionless dynamical variables. The resulting dynamical system approach is "form-invariant" in the sense that one does not require to know the specific functional form of \(f(R)\) a-priori to make the system autonomous. However, the price to pay is that one now requires to impose an algebraic relation between the cosmographic parameters, i.e. specify a certain time evolution of the universe, to make the system autonomous. In this sense, this approach can be complementary to the reconstruction programme in \(f(R)\) gravity. In cases where the reconstruction of \(f(R)\) is in principle possible but the resulting form of \(f(R)\) is not compact or mathematically intractable, our approach can provide interesting insight while altogether avoiding the reconstruction program. We hope this approach may be of interest to the cosmography research community.

In this work, we explore the phenomenon of cosmic evolution using curved FLRW space-time bounded by apparent horizon with a specific holographic cut-off. To this end, we use the framework of Rastall gravity and universe is assumed to be consists of interacting/non-interacting dark energy and dark matter. We evaluate exact solutions of the dynamical equations and constraint the holographic parameter \(c^{2}(z)\) assuming a slowly varying function of red-shift. Moreover, we analyze nature of the obtained results via deceleration parameter, statefinder pair and \(Om(z)\)-diagnostic by constraining the involved model parameters using latest observational data. We conclude that this holographic proposal is enough to describe the cosmic evolution at an accelerating rate.

Maxwell equations and the equations of General Relativity are scale-invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale-invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as a matter is present, the effects of scale invariance rapidly decline from ρ = 0 to the critical density (ρ_c), and are forbidden for densities above ρ_c. The absence of scale invariance, in this case, is consistent with considerations about causal connection. Below ρ_c, scale invariance appears as an open possibility, which also depends on the occurrence of in the scale-invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field φ in the energy density ρ = (1/2)\(\dot{φ}^2\) +V(φ) of the vacuum at inflation. This leads to some constraints on the potential. In the framework of scale invariance, inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ρ_c is an open possibility; the final answer may come from high redshift observations, where differences from the ΛCDM models appear. Published by A. Maeder and V. G. Gueorguiev in MNRAS 504, 4005–4014 (2021)[https://doi.org/10.1093/mnras/stab1102].

We construct Einstein-Gauss-Bonnet gravity models with scalar fields minimally coupled with the Ricci scalar due to the relation between derivatives of the effective potential and the spectral index. We choose models with an exponential potential considering exit from inflation and the slow-roll regime. The coupling function of the Gauss-Bonnet term with the scalar field and the potential can be expressed through the effective potential and the tensor-to-scalar ratio. So, the choice of the tensor-to-scalar ratio leads to expressions for potential and the Gauss-Bonnet coupling function. Moreover, the relation between the tensor-to-scalar ratio and the field derivatives with respect to the e-folding number allows to reconstruct the model in terms of the field. The report is based on arXiv:2105.02772, arXiv:2005.10133.

Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss-Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss-Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential method we construct a set of models with the same values of the scalar spectral index \(n_s\)​ and the amplitude of the scalar perturbations \(A_s\)​ and different values of the tensor-to-scalar ratio \(r\). The talk is based on the papers by E.O. Pozdeeva and S.Yu. Vernov: arXiv:2104.04995 and arXiv:2104.11111.

In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations in a general scalar-torsion theory whose Lagrangian density is an arbitrary function \(f(T,\phi)\) of the torsion scalar \(T\) and a scalar field \(\phi\), plus the kinetic term of this latter. It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations. In order to restore the local Lorentz symmetry, we have incorporated six additional degrees of freedom in the form of Goldstone modes of the symmetry breaking through a Lorentz rotation of the tetrad field. After integrating out all the auxiliary modes, we obtain a second order action for the scalar and tensor propagating modes and their power spectrum generated during inflation. It is found that an explicit mass term emerges in the second order action for curvature perturbation, describing the imprints of local Lorentz violation at first-order of slow-roll. We show that only inflationary models with nonminimal coupling functions \(f(T,\phi)\) which are non-linear in \(T\), including the case of \(f(T)\) gravity with minimally coupled scalar field, can generate primordial fluctuations.

Attractor inflation is a particularly robust framework for developing inflationary models that are insensitive to the details of the potential. Such models are in most cases considered in the metric formulation of gravity. However, non-minimal models may not necessarily maintain their attractor nature in the Palatini formalism where the connection is independent of the metric. In this talk, we examine how the β-function formalism can be used to reconstruct viable inflationary potential in the metric and Palatini approaches. The presentation is based on a paper arxiv: 2103.01182 (by A. Karam, S. Karamitsos, M.Saal).

We reconsider the dynamical systems approach to analyze inflationary universe in the Jordan frame models of scalar field nonminimally coupled to curvature or torsion. The adopted set of variables allows us to clearly distinguish between different asymptotic states in the phase space, including the kinetic and inflationary regimes. Inflation is realized as a heteroclinic trajectory originating either at infinity from a nonhyperbolic asymptotic de Sitter point or from a regular saddle de Sitter point. We also present a comprehensive picture of possible initial conditions leading to sufficient inflationary expansion and show their extent on the phase diagrams. In addition we determine the correct slow roll conditions applicable in the Jordan frame and show how they approximate the leading inflationary "attractor solution". To seek the asymptotic fixed points we outline a heuristic method in terms of the "effective potential" and "effective mass", which can be applied for any nonminimally coupled theories.

Cosmology on a Hubble scale is parameterized by a Friedmann scale factor \(a(t)\), scaled by a closure density \(\rho_c=3H^2/8\pi G\) and de Sitter scale of acceleration \(a_{dS}=cH\), where \(G\) is Newton's constant and \(H=\dot{a}/a\) is the Hubble parameter. In the face of a cosmological horizon, it satisfies a non-dimensional equation of motion \(D(\kappa)=3\Omega_M\), where \(D(u)=\ddot{u}u/\dot{u}^2\) is dimensionless curvature, \(\kappa=1/a\), and \(\Omega_M\) is dimensionless matter density. It satisfies a T-duality invariant \(D(a)+D(\kappa)=2\), where \(D(a)\) is the curvature conventionally used in \(\Lambda\)CDM. Its accelerated expansion exceeds that of \(\Lambda\)CDM by some 10% in \(H_0\), consistent with the Local Distance Ladder yet preserving a canonical age of the Universe, identified with an instability in de Sitter space in the distant future.

We laid the foundation of the Planck 2013 mission’s experiment on the current composition of matter in the Universe—the percentage of visible / baryonic, dark matter and dark energy—in terms of differential geometry, which resulted in a mirror image of the experiment in the form of a stereographic projection. However, we must complement our ʺprojectionʺ with Albert Einstein sentiment: "As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality ".

Our findings confirm Planck’s satellite data, based on which some predictions were made regarding the dynamics of the Universe in its past and future. On the same basis, a new procedure was developed for calculating distances to galaxies without the use of Hubble’s constant. Then, the procedure for calculating distances was compared with the luminosity distances and the Hubble’s law diagram, as well as with an alternative method for calculating distances linearly dependent on the redshift.

Luminosity and Hubble’s law distances for comparative analysis were found in the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technol‐ ogy, under contract with the National Aeronautics and Space Administration. “NASA/IPAC Extragalactic Database (NED) is a master list of extragalactic objects for which cross‐identifications of names have been established, accurate positions and redshifts entered to the extent possible, and some basic data collected.” The results contradict rather than support the use of the Standard Cosmological Model.

We also discussed an experiment comparing the angular diameters of the distances between pairs of quasars based on data from publicly available sources. The evaluations were completed in terms of our new methods, which proved to be acceptable in their theoretical estimate of the comoving angular diameter compared to two independent datasets. It turned out to be possible to apply the Hubble diagram. The Hubble diagram was also used in a comoving manner; however, it underestimated the length of the angular diameter between quasars, while the first method overestimated.

In barmaid language our technique performs +zoom while it performs -zoom at large distances with Hubble diagram. The best fit occurred with the second method. All of our conclusions were based on standard statistical reasoning that coincidence cannot be the result of chance, error, or other reason, but it reflects the fact that calculating the distance to a cosmological object is actually more difficult than most astronomers think.

Keywords: Universe Composition, Quantum Vacuum, Red Shift, Visible Matter, Background Energy‐Field, Quasars

Downloads:

http://www.datalaundering.com/download/CosmologyContradictsCover.pdf

http://www.datalaundering.com/download/Big-Bang-App.pdf

https://www.saxo.com/dk/products/search?query=mullat

http://www.datalaundering.com/download/Landau-Lifshitz-RG.pdf

http://www.datalaundering.com/download/Fundamental-RG.pdf

My presentation: http://www.datalaundering.com/download/Mullat-conference.pdf

• About the author: Former docent at the Faculty of Economics, Tallinn Technical University, Estonia; Independent researcher. Docent is an Eastern European academic title equivalent to Associate Professor in the USA. Residence: Byvej 269, 2650 Hvidovre, Denmark, or Jahu tn.1/2-117, 10415 Põhja Tallinn, Estonia, E‐Mail: mjoosep@gmail.com. Phone: +372 6450027

The current cosmological probes have provided an extraordinary confirmation of the standard LCDM cosmological model, that has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in portion the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this talk I will list a few interesting new physics models in the direction of extended theories of gravity that could solve this tension and discuss how the new computational techniques will be crucial in this role.

We perform observational tests on the $f(T) $ gravity using the Cosmic Chronometer data, SNIa data and BAO data together with three different priors. In this work, we test five \(f(T)\) gravity models using the Markov chain Monte Carlo technique to constrain the varying parameters of the models, including the Hubble constant \(H_0\). These models, in turn, are compared to the \(\Lambda\)CDM model which allows us to investigate the \(H_0\) tension.

Within the theory of General Relativity, the relative motion of test bodies is described by means of the geodesic deviation (Jacobi) equation. This equation only holds under certain assumptions and can be used only for the description of structureless neutral test bodies. Here we present some recent results on generalized deviation equations in a Riemannian as well as in a Riemann-Cartan background, the latter spacetime forms the basis of many modern gravity theories. It is shown, how deviation equations can be used in the construction of the so-called gravitational compass, which allows for an operational determination of the gravitational field.

The parametrized post-Newtonian (PPN) formalism is a valuable tool for assessing the consistence of metric gravity theories with observations in the weak field regime, in particular the solar system and pulsars. Applying the PPN formalism to a particular gravity theory requires deriving a higher-order perturbative expansion of the theory's field equations, and solving these field equations order by order using a particular form of the metric tensor. Since the steps to be applied are similar among different types of gravity theories, performing them with the help of computer algebra comes handy. xPPN is an implementation of the PPN formalism using xAct for Mathematica. In my talk I give a brief overview of the features of xPPN and the range of theories which can be studied so far. I provide an outlook towards future extensions and possible theories they will address.

The talk is based on Eur. Phys. J. C 81 (2021) 504 [arXiv:2012.14984].

In this talk, I would discuss the geometry of compact stellar objects through Noether symmetry approach in the energy-momentum squared gravity. This newly developed theory overcomes the problems of big-bang singularity and provides the viable cosmological consequences in the early time universe. Moreover, its implications occur in high curvature regime where the deviations of energy-momentum squared gravity from general relativity is confirmed. We consider the minimal coupling model of this modified theory and formulate symmetry generators as well as corresponding conserved quantities. We use conservation relation and apply some suitable initial conditions to evaluate the metric potentials. Finally, we explore some interesting features of the compact objects for appropriate values of the model parameters through numeric analysis. It is found that compact stellar objects in this particular framework depend on the model parameters as well as conserved quantities. We conclude that Noether symmetries generate solutions that are consistent with the astrophysical observational data and hence confirms the viability of this procedure.

We examine the evolution of Pre-Main Sequence Stars in the Eddington-inspired Born-Infeld (EiBI) gravity. In particular, we demonstrate that the Hayashi tracks of low-mass stars are shifted in EiBI gravity. This fact, together with the Minimal Main Sequence Mass, will allow us to constrain the theory parameter. We also briefly discuss the radiative core development.

This talk is primarily based on my recent paper IJMPD 30, 05 (2021) 2150034.

Einstein's general theory of relativity is an incredible theory to explain various astrophysical phenomena and early universe cosmology. It provides an immense understanding of the physics of various compact objects, e.g. black holes, neutron stars, white dwarfs, etc. However, some recent observations in cosmology and also compact objects question the complete validity of the general theory of relativity in extremely high-density regions. Moreover, we know that a white dwarf, as it pulls matter from its companion star, gives rise to type Ia supernova (SNIa). At a certain mass, known as Chandrasekhar mass-limit (currently accepted value is \(1.4M_\odot\) for a non-rotating carbon-oxygen white dwarf), white dwarf becomes unstable and it burns out without leaving any remnant behind. Nevertheless, some recent astrophysical observations argue that the value of the Chandrasekhar mass limit has to be violated. Howell et al. (2006), Scalzo et al. (2010), etc. have detected extremely high luminous supernovae which they have argued to be originated from white dwarf of mass as high as \(2.8M_\odot\). It was also found that the decaying tails of these SNeIa have a completely different trend than those for normal SNeIa. A bunch of different theories and models such as the presence of a high magnetic field, modified gravity, total lepton number violation, generalized Heisenberg uncertainty principle, etc. have been proposed by different researchers, with each of these models possess its own limitations. To overcome this difficulty, we propose the idea of noncommutativity in the position and momentum, which will lead to the super-Chandrasekhar mass-limit. The idea of noncommutativity, apart from Heisenberg's uncertainty principle, is there for quite some time, without any observational proof. In my presentation, I will explain how the detection of super-Chandrasekhar white dwarfs can be direct possible evidence of noncommutativity, and thereby it can easily answer various unresolved puzzles such as generation of the primordial magnetic field in the early universe, the importance of standard candles using SNeIa to measure luminosity distances in cosmology, etc.

The GRAVITY collaboration has recently a detected continuous circular relativistic motion during infrared flares of Sgr A*, which has been interpreted as orbital motion near the event horizon of a black-hole. In this work, we use the ray-tracing code GYOTO to analyze the possibility of these observations being consistent with a central bosonic star instead of a black-hole. Our model consists of an isotropically emitting hot-spot orbiting a central boson or Proca star. Images of the orbit at different times and the integrated flux were obtained for both models and compared with the case of a Schwarzschild black-hole. Although the overall qualitative picture is comparable, the bosonic star models present an extra image when the emitting hot-spot passes behind the central object caused by photons travelling through the interior of the star. Furthermore, there are also measurable differences in the angles of deflection, orbital periods, and centroid of the flux, which can potentially be detected.

In the present talk, I will briefly discuss the current status of a certain class of theories where the coupling constants can vary. Particular attention will be devoted to the implementation of such a theory on black hole physics and relativistic stars.

The presence of magnetic fields in a quantum system has the effect of splitting the pressure into two components, one parallel and the other perpendicular to the magnetic field. This anisotropy in the Equations of State (EoS) of compact stars suggests the necessity of using structure equations considering the symmetry of the magnetized system. Starting from an axially symmetric metric in spherical coordinates, the \(\gamma\)-metric, we construct a system of equations to describe the structure of spheroidal compact stars. The model relates the shape of the compact star to the properties of the composing matter by connecting the geometric parameter \(\gamma\) to the source of the anisotropy. In this presentation, I will briefly present the model and the main results obtained for white dwarfs, boson stars and strange quark stars.

We study the gravitational field of an infinitesimally thin spherical shell with fictitious oscillations in the radial directions. These fictitious oscillations are considered as geometrical properties of spacetime that can affect the temporal and spatial measurements by an observer. The metric derived is equivalent to that for a timelike hypersurface with constant mass M. The external spacetime is static and satisfies the Schwarzschild solution. According to Birkhoff’s theorem, this thin shell can be contracted to an infinitesimal radius while the external spacetime is unaffected. The spacetime structure arises from the infinitesimal radius shell with fictitious oscillations can mimic the gravitational field of a point mass in relativity [1]. By analyzing the Fourier decomposition of an oscillation in time that has varying time rates, we show that a proper time oscillator can give rise to the fictitious oscillations on the thin shell with an infinitesimal radius [2].

References: [1] H. Y. Yau, “Thin shell with fictitious oscillations”, in Spacetime Physics 1907 – 2017, Chapter 6 (Minkowski Institute Press, Montreal, 2019) [2] H. Y. Yau, “Schwarzschild field of a proper time oscillator”, Symmetry 12(2), 312 (2020)

We present evidence that semiclassical gravity can give place to ultracompact stars, indistinguishable from black holes up to current observations. We integrate the semiclassical equations of (spherically symmetric) stellar equilibrium for a constant-density classical fluid. The semiclassical contribution is modelled by a quantum massless scalar field in a genuinely-static vacuum state compatible with asymptotic flatness (Boulware vacuum). The Renormalized Stress-Energy Tensor (RSET) is firstly approximated by a cut-off version of the analytic Polyakov approximation. This approximation reveals a crucial difference with respect to purely classical solutions: stars whose compactness is nearing that of a black hole exhibit bounded pressures and curvatures up to central core of a very small relative size. For a subfamily of these ultracompact configurations, their mass can be made arbitrarily close to zero at the boundary of the core, just before the solution enters a singular regime. Our analysis suggests the absence of a Buchdahl limit in semiclasical gravity, while indicating that the cut-off regularized Polyakov approximation must be improved to describe equilibrium configurations of arbitrary compactness that remain regular at the center of spherical symmetry.

In my talk, I will present the relativistic hydrostatic equilibrium equations for a wide class of gravitational theories possessing a scalar-tensor representation. It turns out that the stellar structure equations can be written with respect to the scalar-tensor conformal invariants. Mass-radius relations of homogeneous cold spheres will also be obtained for Palatini \(f(R)\) gravity. Apart from the chemical composition, an additional degeneracy in the profiles is discussed. Moreover, a new test of gravity will be proposed.

The Einstein equations allow two fundamentally different approaches to their study: Either one interprets them strictly as a set of partial differential equations determining the metric from a given stress-energy as source, or one asks which source gives rise to a given input metric. Even modified theories of gravity often allow a reformulation in terms of “effective” stress-energy tensors, thus allowing a direct comparison to general-relativistic predictions. In general, this results in a multitude of metrics of which only few are currently known to have observational and experimental relevance. Especially in mathematical relativity one key ingredient to separate the good, the bad, and the ugly stress-energy tensors (in either interpretation) that arose are the various energy conditions. In this talk I will give a short review of their status, with a particular focus on the recently and prominently resurfaced “warp drive metrics”.

Black holes are the purest expression of gravity and at the same time the places where our best theory of gravitation, Einstein General Relativity, meets its demise in the form of singularities. We know, however, that any successful theory of quantum gravity should be able to resolve these uncharted regions, but can they do so without showing any modification outside the event horizon? can real black holes be undistinguishable from the one predicted by general relativity? The recent direct observation of these tantalising objects represents an unprecedented possibility to answer these questions. In this talk, we shall explore on general grounds what alternative objects we can expect from a quantum gravity induced regularisation of singularities and discuss what observations can or will tell us about their nature.

A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach, the dynamical variable encoding the properties of the system is the so-called 1-particle distribution function (1PDF), which is a scalar density on the space of allowed particle positions and velocities - i.e. on the tangent bundle of the spacetime manifold. Yet, when the gravitational field of a kinetic gas is derived in general relativity (via the Einstein-Vlasov equations), the information about the velocity distribution of the gas particles is averaged out and therefore lost. We argue that a more appropriate theory of gravity, that fully takes the velocity distribution into account, must be also modeled on the tangent bundle of spacetime and that the most natural mathematical framework for this task is Finsler geometry. Following this line of thought, we construct a coupling between the kinetic gas and a recently proposed Finsler geometric extension of general relativity. Also, in view of cosmological applications, we briefly discuss spatially homogeneous and isotropic Finsler spacetimes.

References: 1. M. Hohmann, C. Pfeifer, N. Voicu, The kinetic gas universe, European Physical Journal C 80, 809 (2020), arXiv:2005.13561v2 [gr-qc]. 2. M. Hohmann, C. Pfeifer, N. Voicu, Kinetic gases as direct gravity sources, Physical Review D 101, 024062 (2020), arXiv:1910.14044v2 [gr-qc]. 3. M. Hohmann, C. Pfeifer, N. Voicu, Cosmological Finsler spacetimes, Universe 6 (5), 65 (2020), arXiv:2003.02299v2 [gr-qc].

We will present a \(\kappa\)-Poincaré invariant (noncommutative) gauge theory on \(\kappa\)-Minkowski space. Within a natural differential calculus based on a distinguished set of twisted derivations belonging to the algebra of deformed translations, combined with a twisted extension of the notion of connection, we will show that \(d=5\) is the unique value for the classical dimension at which the gauge action supports both the gauge invariance and the \(\kappa\)-Poincaré invariance. We will comment on phenomenological consequences and accessible observables.

Recently, an increasing group of theorists, experimentalists, and observational astronomers have been working on searches for tiny hypothetical deviations from the spacetime symmetries of General Relativity, including local Lorentz symmetry. Many areas in both ground-based experiments, space-based tests and astrophysical observations have been used for tests and analyses. Despite the many null results in different sectors, to date, many areas remain unexplored. In this talk, we present an overview of the theory and phenomenology of precision tests of local Lorentz symmetry in gravity. Recent precision tests of local Lorentz symmetry in gravitational waves, pulsar observations, lunar laser ranging, and other areas are discussed.

In this talk, I will consider a deformed kinematics that goes beyond special relativity as a way to account for possible low-energy effects of a quantum gravity theory that could lead to some experimental evidences. This can be done while keeping a relativity principle, an approach which is usually known as doubly (or deformed) special relativity. In this context, I will give a simple geometric interpretation of the deformed kinematics and explain how it can be related to a metric in maximally symmetric curved momentum space. Moreover, this metric can be extended to the whole phase space, leading to a notion of spacetime. Also, this geometrical formalism can be generalized in order to take into account a space-time curvature in a simple way, leading to a momentum deformation of general relativity. I will explain theoretical aspects and possible phenomenological consequences of such deformation.

Modified dispersion relations are one way to effectively capture effects of quantum gravity on high energetic particles propagating through spacetime. In this talk I will present the predictions for the time delay in the lifetime of elementary particles on flat spacetime as well as photon orbits, the Shapiro delay and light deflection in spherically symmetric spacetimes from first order Plank scale modified dispersion relations, with focus in the kappa-Poincare dispersion relation. In addition the relation between modified dispersion relations and Finsler geometry will be highlighted.

Amongst myriad of alternative theories of gravity, the canonical theory was established at GFOG17 [https://inspirehep.net/literature/1652843].

More recently, a completely new approach towards an ultraviolet completion of the theory has been discovered: M_Planck is the mass of the gravitational connection, and therefore integrability and thus spacetime is lost at the ultramicroscopic scales 1/M_Planck.

A brief motivation of why gauge CPT should be considered as a natural extension of general relativity is presented. Links to two arXiv papers are given. Also, a link is given to the paper (and its YouTube presentation) “The baryonic Tully-Fisher law and the Gauge Theory of CPT Transformations” published and presented at the Proceedings of the International Conference: Cosmology on Small Scales 2020, Excessive Extrapolations and Selected Controversies in Cosmology, Prague, September 23-26, 2020.

On one hand, the formalism developed in thermodynamics of spacetime allows a derivation of Einstein equations from the proportionality of entropy to the area. On the other hand, low energy quantum gravity effects imply a modified entropy formula with an additional term logarithmic in the area. Combining both concepts, I will introduce the derivation of quantum modified gravitational dynamics from the modified entropy and discuss its main features. Moreover, I will show its physical implications on a simple cosmological model and show that it suggests the replacement of the Big Bang singularity by a regular bounce. The talk is based on A. Alonso-Serrano, M. Liška, "Quantum phenomenological gravitational dynamics: a general view from thermodynamics of spacetime", JHEP 2020, 196 (2020).

We study the morphology of the bouncing cosmology that emerges in the semiclassical and quantum implementation of Polymer Quantum Mechanics on the Hamiltonian formulation of the Friedmann-Lemaitre-Robertson-Walker model both in terms of the Ashtekar-Barbero-Immirzi connection and of the generalized coordinate conjugate to the Universe volume. The Big Bounce results to be an intrinsic cut-off on the cosmological dynamics only in the second case, while in terms of the standard connection the Universe density at the Bounce depends on the initial conditions for the prepared wave packet. In Loop Quantum Cosmology the same difference in the nature of the Big Bounce is associated to introducing the Area Gap, i.e. the cut-off on the geometric operators from full Loop Quantum Gravity, in a comoving or in a physical spacetime metric. The privileged character of the Ashtekar-Barbero-Immirzi connection in Loop Quantum Gravity, together with the results from the Polymer quantization, suggest that the preferable scenario should a Big Bounce that is not a Universal cut-off but uses variables linked to the proper SU(2) connection.

Quantum physics removes classical singularities by restricting the spectrum of physical quantum states. We present a simple quantum description supporting the idea that black holes are macroscopic quantum objects with a typical width comparable with their horizon radius. The effective spacetime geometry is described as a coherent state of gravitons which cannot resolve the classical central singularity because it does not contain modes of arbitrarily short wavelength. Corrections to the Schwarzschild geometry are then estimated, which could result in observable effects for the gravitational collapse of compact objects and both astrophysical and microscopic black holes.

The standard formulation of General Relativity is based on a geometrical framework where the spacetime manifold is endowed with a Lorentzian metric and its associated Levi-Civita connection. However, the independent nature of the metric and affine structures of spacetime grants the metric-affine arena where the torsion and the non-metricity are brought into play. After briefly discussing how these two actors can provide equivalent descriptions of GR, I will discuss pathological encounters when exploring theories beyond Einstein's shelter in the metric-affine landscape.

We derive the gravitational energy momentum tensor for a general Lagrangian of any order and prove that this tensor, in general, is not covariant but only affine, then it is a pseudo-tensor. Furthermore, the pseudo-tensor is calculated in the weak field limit up to a first non-vanishing term of second order in the metric perturbations. The average value of the pseudo-tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle carried by a gravitational wave. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with non-local theories of gravity. The general aim of the approach is to deal with theories of any order under the same standard.

We find ghost-free theories of Poincare gauge gravity describing a massive spin-2 field in addition to the massless graviton. The theories are found by utilizing the equivalent to ghost-free massive bigravity and, accordingly, are free from ghost at fully non-linear orders. In three dimensions, the Lagrangian is at most quadratic in the curvature and the torsion while an infinite number of higher curvature terms is needed to make it ghost-free in four dimensions. We briefly discuss its implication to the AdS/CFT correspondence and the relation to Weyl square gravity in the metric formalism.

I will give an overview of problems and features we see now in the modified teleparallel models, such as f(T). The news will be both good (generalised Bianchi identity, progress on spherically symmetric solutions, predictions of gravitational slip) and bad (not well-defined number of degrees of freedom, strong coupling in physically interesting cases, strange behaviour of the new mode(s) even around slightly deformed backgrounds). I will also discuss covariantisation with respect to Lorentz. In our opinion, it is not of a big difference, but can give some technical advantages. Finally, I will give an outlook on what would be good to do now and what to expect.

The tetrad formulation of gravity has deficiencies, which are causing confusion in teleparallel theories, in relation to so-called “Lorentz gauge transformations”. By using coset space methods, devised for describing non-linearly realised internal symmetries, these problems can be resolved. This provides a geometric meaning to the “Lorentz gauge transformations”, as the relation between different parallelisms. It naturally separates out these parallelism degrees of freedom from the metric degrees of freedom, which allows a Cartan decomposition of the Weitzenböck connection.

This new formulation of gravitational theories shows that the Weitzenböck gauge is coordinate-dependent. Inertial effects are found to be associated with the metric degrees of freedom, not the so-called “Lorentz gauge transformations”. The presentation is based on Sections 1-5 of Tangent space symmetries in general relativity and teleparallelism.

We show that the Kerr-Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr-Schild null vector, and describe the solution for a rotating black hole in this framework. It is shown that the solution depends on the chosen tetrad in a non-trivial way if the spin connection is fixed to be the one of the flat background spacetime. We show furthermore that any Kerr-Schild solution with a flat background is also a solution of f(T) gravity. Based on arXiv:2103.02620.

We examine the possibility of finding exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lema^tre-Tolman-Bondi (LTB) dust models. We apply to the LTB metric, as obtained from the Schwarzschild solution in General Relativity, the formalism of Teleparallel Gravity in its extension to \(f(T,B)\) models.

Teleparalell gravity and cosmology has captured a lot of attention in the community in recent years with a drastic increase in related publications and collaborations. In this context, it is timely to review the state of the art in the field and to connect this progress with foundational developments aimed at resolving a number of misconceptions in the literature. In this Review, we also highlight recent progress on the observational sector and possible ways forward in that direction, including possible hints of modified gravity from machine learning. In this short presentation, we highlight some of these advances and expand on the motivation for this new review in teleparallel gravity and cosmology.

Index theory deals with solutions of certain differential equations, where an index roughly measures the difference between the number of kernel solutions and constraints coming from inhomogeneities. The famous Atiyah-Singer index theorem states, that for an elliptic operator this number can be expressed with topological data of the underlying (compact) Riemannian manifold - generalizations to singular and non-compact Riemannian spaces are known and well studied. Next to an analytical interest the index also appears formally in the study of anomalies in relativistic quantum field theories, where the underlying manifold is Lorentzian and the operator of interest usually hyperbolic. A rigorous treatment of these anomalies were not clear until the groundbreaking result of Bär and Strohmaier in 2015. Since then several extensions and applications have been discussed and are supposed to play a crucial role in the future analysis of quantum anomalies on globally hyperbolic spacetimes as well as differential geometry of pseudo-Riemannian manifolds. After introducing terminology and examples of quantum anomalies, related to a (local) index, I will explain the result of this Lorentzian index theorem, mention its application to a certain chiral anomaly and several extensions to non-compact Lorentzian spaces, where we studied the case, that the globally hyperbolic manifold is spatially a Galois covering. The proof of the theorems will be shown without details for this particular case, as they are related by a similar strategy and contain interesting intermediate results.

We test our recently developed approach of constructing conserved quantities in Teleparallel Equivalent of General Relativity (TEGR) by calculating energy characteristics for Schwarzschild black hole (SBH). Conserved currents and related superpotentials are coordinate covariant and invariant with respect to local Lorentz rotations of tetrads due to introducing an inertial spin connection (ISC) which is not a dynamical variable. As an external requirement, to define the ISC we use "turning off gravity" principle. We examine the values of the total (global) energy of SBH and the energy density measured by a freely falling observer in the field of SBH. Different coordinates and frames for SBH initiate different definitions of ISC with the use of the "turning off gravity" principle. The different choice of ISC leads to the different results. The main goal of the research is searching for the most appropriate ISC for SBH.
Starting from the standard Schwarzschild metric and deriving the related ISC, we obtain the correct SBH mass, but a freely falling observer measures non-zero energy density that contradicts the equivalence principle. Basing on the Lemaitre metric and its related ISC we have the consistency with the equivalence principle, but do not get the correct mass. Only after constructing new generalized Lemaitre metric (assuming the free falling with arbitrary energy) the problem has been resolved. The new ISC is different from others found before, and using it we get both the correct mass and compliance with the equivalence principle.
The novelty is in the following: 1) purely Lemaitre presentation of BH has been used in TEGR firstly; 2) the new generalized Lemaitre metric and tetrad has been constructed; 3) the generalized Lemaitre presentation in TEGR has resolved the aforementioned outstanding problems; 4) the definitions of ISC in TEGR and in f(T) theories are compared; 5) the results help us to understand more on the SBHs themselves.

In this talk, I will construct a novel three-dimensional teleparallel supergravity theory in three dimensions. I will show how a teleparallel algebra can be obtained by deforming the Poincaré algebra. A supersymmetric extension will be defined and a new supergravity theory will be constructed as a Chern-Simons action. The teleparallel supergravity action is characterized by a non-vanishing super-torsion and reproduces the standard Poincaré supergravity in the vanishing cosmological limit. The extension of our results to N supersymmetries is also discussed.

The conventional action formulation for general relativity is by the Einstein-Hilbert action, which depends on the Levi-Civita connection and the metric. However, a classically equivalent theory can be done by formulating the action in terms of torsion (related to the antisymmetric part of the affine connection) and tetrads. This is done in the theory called . From this formulation as a starting point it is not evident from a quick look that this theory should be selected in favor of other modified teleparallel theories of gravity. This gives a motivation from a fundamental point of view to investigate the theory further, where the Hamiltonian analysis is useful since it can give insights of the canonical structure of a theory.

In the literature there are some work on the Hamiltonian analysis for the most basic teleparallel theories of gravity. However, they are either incomplete, contradicting to other work, not formulated in a covariant way, or a combination of these. In this talk I will outline the derivation of the so-called primary Hamiltonian for the most basic covariant teleparallel theories of gravity. I explicitly write out these Hamiltonians without putting the so-called spin connection to zero. Then, I will briefly talk about perturbations in the aforementioned theories and use this to show that they are most likely not viable theories. The irreducible decomposition of the torsion scalar will be discussed in order to reach some insights on the fundamental relevance for the irreducible components and their relation to propagating fields.

We present the current understanding of the constraint structure of modified teleparallel theories of gravity, which is crucial to understand the role of local Lorentz transformations in both pure-tetrad and covariant formalisms of the theory. The nonlinear constraint effect produces a change in the rank of the matrix of Poisson brackets among constraints, which subsequently generates jumps in the number of degrees of freedom. These can be an indication of troubles with consistency, therefore, understanding these theoretical issues are critical to cure potential strong coupling problems, and for studying the viability of not only teleparallel but other modified gravities as well.

The junction conditions formalism is needed whenever two patches of space-times are matched at a given hypersurface across of which discontinuties in several geometrical and matter quantities may occur. We discuss the shape of such conditions for metric-affine theories of gravity, where metric and affine connection are independent entities. Furthermore, we implement several application of these conditions, including stellar surfaces, thin-shell wormholes, and new observational signals in terms of double shadows from asymmetric wormholes.