General Relativity and Quantum Cosmology (gr-qc)

Abstract: GW191219\_163120 is a gravitational wave signal that is believed to have originated from a neutron star-black hole (NSBH) coalescence with an extreme mass ratio. In this work, we use data of GW191219\_163120 from LIGO and Virgo to test the first law of black hole mechanics by considering the neutron star as a perturbation to the black hole before the merger, and the remnant black hole as a stationary black hole after the merger. Our results demonstrate consistency with the first law of black hole mechanics, with an error level of about 6\% at 68\% credibility and 10\% at 95\% credibility. We also find that the higher the mass ratio of the gravitational wave source, the more consistent our results are with the first law of black hole mechanics. Overall, our study sheds light on the nature of NSBH coalescences and their implications for black hole mechanics.

Abstract: We find three new exact solutions of the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally hyperbolic spacetimes in which almost abelian Lie groups act on the spaces isometrically and simply transitively. We give left-invariant metrics on the spaces and solve Ricci-flat conditions of the spacetimes. In the four-dimensional case, our solutions correspond to the Bianchi type II vacuum solution. By our results and previous studies, all spatially homogeneous solutions whose spaces have zero-dimensional moduli spaces of left-invariant metrics are found. For the simplest solution, we show that each of the spatial dimensions cannot expand or contract simultaneously in the late-time limit.

Abstract: Buchdahl stars are defined by the saturation of the Buchdahl bound; the gravitational potential felt by a radially falling particle is less than equal to 4/9. An interesting alternative characterization is given by gravitational energy being half of non-gravitational energy. With insightful identification of the former with kinetic and the latter with potential energy, it has been recently argued that the equilibrium of a Buchdahl star may be governed by the Virial theorem. In this essay, we provide a purely geometric version of this theorem and thereby of the Buchdahl star characterization. We show that a collapsing star maintaining the Virial equilibrium must expel energy via heat flux, appearing in the exterior as Vaidya radiation, and it escapes getting trapped into a black hole.

Abstract: The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor non-metricity are excluded. The manifestly covariant gauge process is based on canonical transformations in the De Donder-Weyl Hamiltonian formalism, starting from a small number of basic postulates. Thereby, the original system of matter fields in flat spacetime, represented by non-degenerate Hamiltonian densities, is amended by spacetime fields. The coupling of matter and spacetime fields leaves the action integral of the combined system invariant under active local Lorentz transformations and passive diffeomorphisms, aka Principle of General Relativity. We consider the Klein-Gordon, Maxwell-Proca, and Dirac fields and derive the corresponding equations of motion. Albeit the coupling of the given matter fields to the gauge fields are unambiguously determined by CCGG, the dynamics of the free gauge fields must be postulated based on physical reasoning. Our choice allows to derive Poisson-like equations of motion also for curvature and torsion. The latter is proven to be totally anti-symmetric. The affine connection is a function of the spin connection and vierbein fields. Requesting the spin connection to be anti-symmetric gives naturally metric compatibility. The canonical equations combine to an extension of the Einstein-Hilbert action with a quadratic Riemann-Cartan concomitant that endows spacetime with inertia. Moreover, a non-degenerate, quadratic version of the free Dirac Lagrangian is deployed. When coupled to gravity, the Dirac equation is endowed with an emergent mass parameter, a curvature-dependent mass correction, and novel interactions between particle spin and spacetime torsion.

Abstract: Symmetric teleparallel gravity offers to reformulate the gravitational formalism without the presence of curvature and torsion with the help of non-metricity tensors. Interestingly, Symmetric teleparallel gravity can be formulated equivalently to teleparallel gravity or general relativity for an appropriate setup. In this study, our aim lies in exploring the bouncing cosmologies as an alternative to the initial singularity of the Universe in the background of modified symmetric teleparallel gravity. To explore this, we adopt the reconstruction technique to present the possible reconstructed Lagrangian for various cosmological bouncing solutions in a flat Friedmann-Lema\^itre-Robertson-Walker spacetime with a perfect fluid matter distribution. We study the reconstructed gravitational Lagrangians, which are capable of reproducing analytical solutions for \textit{symmetric bounce}, \textit{super-bounce}, \textit{oscillatory bounce}, \textit{matter bounce}, and \textit{exponential bouncing} model settings. Further, we examine the dark energy profiles of the models using reconstructed Lagrangians. In addition, we found that an additional term arises in each reconstructed Lagrangian compared to general relativity (GR). That extra term corrected the background GR to present bouncing cosmology in modified gravity. These newly motivated cosmological models may have an effect on gravitational phenomena at other cosmological scales.

Abstract: The quasi-normal mode (QNM) spectrum of black holes is unstable under small perturbation of the potential and has observational consequences in time signals. Such signals might be experimentally difficult to observe and probing this instability will be a technical challenge. Here we investigate the spectral instability of time-independent data. This leads us to study the Regge Poles (RP), the counterparts to the QNMs in the complex angular momentum plane. We present evidence that the RP spectrum is unstable but that not all overtones are affected equally by this instability. Furthermore, the RP spectrum appears somehow more robust than its QNM counterpart. In addition, we reveal that behind this spectral instability lies an underlying structure. The RP spectrum is perturbed in such a way that one can still recover stable scattering quantities using the complex angular momentum approach. We argue that physical stability might be the root of the superior robustness of the RP spectrum.

Abstract: It is well-known that the mass of a non-asymptotically flat spacetime cannot be uniquely defined. A reasonable definition of mass for the Kerr-AdS black hole has been found and widely used in studying black hole thermodynamics. However, the derivation usually needs a background subtraction to eliminate the divergence. It is also unknown whether this formula can be extended to a more general form. In this paper, we provide a more straightforward derivation for the mass formula, only demanding that the first law of black hole thermodynamics and Smarr formula are satisfied. We first make use of the Iyer-Wald formalism to derive a first law of charged Kerr-AdS black hole in the extended phase space. However, this mass is obviously not integrable. We then modify the coefficients of the first law to make the mass integrable. Finally, by applying the scaling argument to the modified first law, we obtain the Smarr formula, i.e., the explicit form of the mass. Remarkably, our mass formula contains a free parameter and when it is set to zero, we recover the familiar mass $M/\Xi^2$ in the literature. Moreover, by making use of the gauge freedom of the Killing vector field $\ppa{t}{a}$, we find a favorite parameter $t'$ which just gives the first law and makes the mass integrable. The mass also satisfies the Smarr formula and takes the form $M/\Xi^{3/2}$. To the best of our knowledge, this is a new mass formula and could have important applications in future studies.

Abstract: In a large class of nonlocal as well as local higher derivative theories minimally coupled to the matter sector, we investigate the exactness of two different classes of homogeneous G\"{o}del-type solutions, which may or may not allow closed time-like curves (CTC). Our analysis is limited to spacetimes solving the Einstein's EoM, thus we can not exclude the presence of other G\"{o}del-type solutions solving the EoM of local and nonlocal higher derivative theories but not the Einstein's EoM.It turns out that the homogeneous G\"{o}del spacetimes without CTC are basically exact solutions for all theories, while the metrics with CTC are not exact solutions of (super-)renormalizable local or nonlocal gravitational theories. Hence, the quantum renormalizability property excludes theories suffering of the G\"{o}del's causality violation. We also comment about nonlocal gravity non-minimally coupled to matter. In this class of theories, all the G\"{o}del's spacetimes, with or without CTC, are exact solutions at classical level. However, the quantum corrections, although perturbative, very likely spoil the exactness of such solutions. Therefore, we can state that the G\"{o}del's Universes with CTC and the super-renormalizability are mutually exclusive.

Abstract: We analyse the response of a comoving local quantum probe, modelled as an Unruh-DeWitt detector coupled to a massive scalar field, in (1+1)-dimensional spatially homogeneous locally de Sitter cosmologies with compact spatial sections, allowing for the scale factor hyperbolic cosine, hyperbolic sine, and exponential evolution laws, as inherited from different local foliations of the de Sitter geometry. For the sinh and exp scale factors, we consider adiabatic vacua in the past, identifying an ambiguity due to a massive zero mode, while for the cosh and sinh expansion laws, we consider large momentum adiabatic vacua and states induced from the Euclidean vacuum; for the latter, we also evaluate the expectation value of the field's stress-energy tensor. Numerical plots are given in selected parameter regimes.

Abstract: We investigate the circular motion and chaos bound of a charged particle near 4D charged AdS black holes in Einstein-Gauss-Bonnet gravity theory. By means of the Jacobian matrix, the analytical form of the Lyapunov exponent of the charged particle is constructed, which satisfies the upper bound when it is on the event horizon. By further expanding the Lyapunov exponent near the horizon and investigating a 4D charged Einstein-Gauss-Bonnet-AdS black hole with different Gauss-Bonnet coupling constant, we find that it has some specific values to determine whether a violation of chaos bound. Besides, we find that in contrast to the static equilibrium, the circular motion of charged particle can have a larger Lyapunov exponent due to the existence of angular momentum. Moreover, we show that the black hole gets closer to the extremal state as the Gauss-Bonnet coupling constant increases, and the bound is more easily violated. In addition, the range of particle charge that may violate the chaotic bound are found for different Gauss-Bonnet coupling constants. The results show that as the GB coupling parameter increases, the value of particle charge required to satisfy the violation of the chaos bound is even smaller.