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General Relativity and Quantum Cosmology (gr-qc)

Thu, 01 Jun 2023

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1.Hawking radiation from stationary black holes using gravitational anomaly

Authors:Selim Sk, Sudipta Sarkar

Abstract: Among all the different techniques to derive the Hawking effect, the approach based on gravitational anomaly by Robinson and Wilczek provides a simple and satisfactory origin of the black hole radiation. In this picture, the effective near horizon physics becomes chiral and contains gravitational anomaly. Nevertheless, the underlying description must be generally covariant, and therefore we require a compensating energy-momentum flux whose divergence cancels the anomaly at the horizon. Remarkably, the energy flux associated with the Hawking emission from the horizon exactly cancels the gravitational anomaly and restores the general covariance at the quantum level. In this work, we present a generalization of the original derivation for a stationary axisymmetric black hole solution of any gravity theory which differs perturbatively from general relativity. The crucial input of the calculation is a remarkable simplification of the near horizon geometry and the validity of the zeroth law of black hole mechanics.

2.Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order

Authors:David Trestini

Abstract: We compute the gravitational waves generated by compact binary systems in a class of massless scalar-tensor (ST) theories to the 1.5 post-Newtonian (1.5PN) order beyond the standard quadrupole radiation in general relativity (GR). Using and adapting to ST theories the multipolar-post-Minkowskian and post-Newtonian formalisms originally defined in GR, we obtain the tail and non-linear memory terms associated with the dipole radiation in ST theory. The multipole moments and GW flux of compact binaries are derived for general orbits including the new 1.5PN contribution, and comparison is made with previous results in the literature. In the case of quasi-circular orbits, we present ready-to-use templates for the data analysis of detectors, and for the first time the scalar GW modes for comparisons with numerical relativity results.

3.Gravitational-wave tails of memory at 4PN order

Authors:David Trestini, Luc Blanchet

Abstract: We study a novel cubic nonlinear effect, the tails-of-memory, which consist of a combination of the tail effect (backscattering of linear gravitational waves against the curvature of spacetime generated by the source) and the memory effect (due to reradiation of gravitational waves by linear gravitational waves themselves). Our final result is consistent with a straightforward direct computation of the memory effect, but also involves many non-trivial tail-like terms.

4.Cosmological models with arbitrary spatial curvature in the theory of gravity with non-minimal derivative coupling

Authors:Sergey V. Sushkov, Rafkat Galeev

Abstract: We investigate isotropic and homogeneous cosmological scenarios in the scalar-tensor theory of gravity with non-minimal derivative coupling of a scalar field to the curvature given by the term $(\zeta/H_0^2) G^{\mu\nu}\nabla_\mu\phi \nabla_\nu\phi$ in the Lagrangian. In general, a cosmological model is determined by six dimensionless parameters: the coupling parameter $\zeta$, and density parameters $\Omega_0$ (cosmological constant), $\Omega_2$ (spatial curvature term), $\Omega_3$ (non-relativistic matter), $\Omega_4$ (radiation), $\Omega_6$ (scalar field term), and the universe evolution is described by the modified Friedmann equation. In the case $\zeta=0$ (no non-minimal derivative coupling) and $\Omega_6=0$ (no scalar field) one has the standard $\Lambda$CDM-model, while if $\Omega_6\not=0$ -- the $\Lambda$CDM-model with an ordinary scalar field. The situation is crucially changed when the scalar field possesses non-minimal derivative coupling to the curvature, i.e. when $\zeta\not=0$. Now, depending on model parameters, (i) There are three qualitatively different initial state of the universe: an eternal kinetic inflation, an initial singularity, and a bounce. The bounce is possible for all types of spatial geometry of the homogeneous universe; (ii) For all types of spatial geometry, the universe goes inevitably through the primary quasi-de Sitter (inflationary) epoch when $a(t)\propto e^{h_{dS}(H_0t)} $ with the de Sitter parameter $h_{dS}^2={1}/{9\zeta}-{8\zeta\Omega_2^3}/{27\Omega_6}$. The mechanism of primary or kinetic inflation is provided by non-minimal derivative coupling and needs no fine-tuned potential; (iii) There are cyclic scenarios of the universe evolution with the non-singular bounce at a minimal value of the scale factor, and a turning point at the maximal one; (iv) There is a natural mechanism providing a change of cosmological epochs.

5.Stability, quasinormal modes in a charged black hole in perfect fluid dark matter

Authors:Anish Das, Anirban Roy Chowdhury, Sunandan Gangopadhyay

Abstract: In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy ($E$) and angular momentum ($L$) in terms of the radius ($r_c$) of the circular orbits. The existence and finite-ness of $E$ and $L$ constrain the possible range of PFDM parameter ($\chi$) and the radius of the circular orbit ($r_c$). We then use the Lyapunov exponent ($\lambda$) to study the stability of the geodesics. Then we analyze the critical exponent ($\gamma$) useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinrmal mode (QNM) frequencies and their dependence on PFDM parameter $\chi$ and black hole charge $Q$. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on $\chi$ and $Q$. Finally, we evaluate the black hole shadow radius $R_s$ and graphically observe the effect of $\chi$ and $Q$ on it.

6.A Cosmological Unicorn Solution to Finsler Gravity

Authors:Sjors Heefer, Christian Pfeifer, Antonio Reggio, Andrea Fuster

Abstract: We 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. Interestingly we find that these solutions have a physically viable light cone structure, even though in some cases the signature is not Lorentzian but positive definite. We furthermore find a promising analogy between our solutions and classical FLRW cosmology. One of our 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. We show that this conformal factor can be interpreted as the scale factor, we compute it as a function of cosmological time, and we show that it corresponds to a linearly expanding (or contracting) Finsler universe.

7.Gravitational collapse of matter in the presence of Quintessence and Phantom-like scalar fields

Authors:Priyanka Saha, Dipanjan Dey, Kaushik Bhattacharya

Abstract: In this work, we propose a model of the gravitational collapse of dark matter in the presence of quintessence or phantom-like scalar fields. Our treatment is based on the principles of general relativity up to virialization. We have chosen a spherical patch that starts to collapse gravitationally as it happens in top-hat collapse. It is seen that although the dark matter sector collapses the dark energy sector does keep a profile that is almost similar to the dark energy profile for the background expanding Friedmann-Lemaitre-Robertson-Walker (FLRW) universe for suitable model parameters. It is observed that in order to formulate the problem in the general relativistic setting one has to abandon the idea of a closed FLRW isolated collapsing patch. General relativity requires an external generalized Vaidya spacetime to be matched with the internal spherical patch whose dynamics is guided by the FLRW metric. It is shown that almost all collapses are accompanied by some flux of matter and radiation in the generalized Vaidya spacetime. Some of the spherical regions of the universe are seen not to collapse but expand eternally, producing void-like structures. Whether a spherical region will collapse or expand depends upon the initial values of the system and other model parameters. As this work shows that collapsing structures must emit some form of radiation, this may be taken as an observational signature of our proposal.

8.Geometrothermodynamic cosmology

Authors:Orlando Luongo, Hernando Quevedo

Abstract: We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical thermodynamics with respect to Legendre transformations, which means that the properties of the systems do not depend on the choice of the thermodynamic potential. Moreover, we show that in geometrothermodynamics it is possible to apply a variational principle to generate thermodynamic fundamental equations, which can be used in the context of relativistic cosmology to generate cosmological models. As a particular example, we consider a fundamental equation that relates the entropy with the internal energy and the volume of the Universe, and construct cosmological models with arbitrary parameters, which can be fixed to reproduce the main aspects of the inflationary era and the standard cosmological paradigm.

9.Constraining Palatini gravity with GR-independent equations of state

Authors:Eva Lope-Oter, Aneta Wojnar

Abstract: We demonstrate how to construct GR-independent equations of state. We emphasize the importance of using theory-based principles instead of relying solely on astrophysical observables and General Relativity (GR). We build a set of equations of state based on first principles, including chiral perturbation theory and perturbation theory in quantum chromodynamics. Interpolation methods are employed to assume thermodynamic stability and causality in the intermediate region. These equations of state are then used to constrain quadratic Palatini $f(\mathcal R)$ gravity, indicating that the parameter lies within the range $-6.47 \lesssim \beta \lesssim 1.99$ km$^2$. Additionally, we briefly discuss the problem of phase transitions and twin stars.

10.Cosmology in the Lorentz gauge theory

Authors:Tomi Koivisto

Abstract: This proceeding is an introduction to cosmological applications of the Lorentz gauge theory. It provides the ingredients for a unique, though yet tentative $\Lambda$CDM theory cosmology. The emergence of spacetime is described by the spontaneous symmetry breaking called here the khronogenesis. Space is then associated with the field strength of the antiself-dual gauge potential, and gravity is associated with the self-dual field strength. In the cosmological setting, khronogenesis seems to predict inflation. It is shown that the Lorentz gauge theory allows the consistent description of spin currents which could have important roles in cosmological phenomenology.