General Relativity and Quantum Cosmology (gr-qc)

Abstract: A charge accelerating in a straight line following the Schwarzschild-Planck moving mirror motion emits thermal radiation for a finite period. Such a mirror motion demonstrates quantum purity and serves as a direct analogy of a black hole with unitary evolution and complete evaporation. Extending the analog to classical electron motion, we derive the emission spectrum, power radiated, and finite total energy and particle count, with particular attention to the thermal radiation limit. This potentially opens the possibility of a laboratory analog of black hole evaporation.

Abstract: We investigate the existence of anisotropic self-similar exact solutions in symmetric teleparallel $f\left( Q\right)$-theory. For the background geometry we consider the Kantowski-Sachs and the Locally Rotationally Symmetric Bianchi type III geometries. These two anisotropic spacetimes are of special interest because in the limit of isotropy they are related to the closed and open Friedmann--Lema\^{\i}tre--Robertson--Walker cosmologies respectively. For each spacetime there exist two distinct families of flat, symmetric connections, which share the symmetries of the spacetime. We present the field equations, and from them, we determine the functional form of the $f\left( Q\right)$ Lagrangian which yields self-similar solutions. We initially consider the vacuum case and subsequently we introduce a matter source in terms of a perfect fluid. Last but not least, we report some self-similar solutions corresponding to static spherically symmetric spacetimes.

Abstract: In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextentability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in $L^p$. Lipschitz continuity is the threshold regularity for causal structures, and curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity $W^{1,p}_\text{loc}$, proves in the affirmative this SCC conjecture with bounded curvature for $p$ sufficiently large, ($p>4$ with uniform bounds, $p>2$ without uniform bounds).

Abstract: The tidal response of compact objects in an inspiraling binary system is measured by a set of tidal Love and dissipation numbers imprinted in the gravitational waveforms. While a four-dimensional black hole in vacuum within General Relativity has vanishing Love numbers, a black hole in alternative theories of gravity can acquire non-vanishing Love numbers. The dissipation numbers may quantify Planckian corrections at the horizon scale. These properties will allow a test of classical theories of gravity in the strong-field regime with gravitational-wave observation. Since black holes are not in the exact vacuum environment in astrophysical situations, the following question arises: can the environment affect the tidal response? In this paper, we investigate the stability of the tidal response of a Schwarzschild black hole for frequency-dependent tidal-field perturbations against a small modification of the background. Our analysis relies on the scattering theory, which overcomes difficulties in defining the relativistic tidal Love numbers. The tidal Love and dissipation numbers can be extracted from the phase shift of sufficiently low-frequency scattering waves. We show that the tidal Love numbers are sensitive to the property of the modification. Therefore, we need careful consideration of the environment around the black hole in assessing the deviation of the underlying theory of gravity from General Relativity with the Love numbers. The modification has less impact on the dissipation numbers, indicating that quantifying the existence of the event horizon with them is not spoiled. We also demonstrate that in a composite system, i.e., a compact object with environmental effects, the Love and dissipation numbers are approximately determined by the sum of the numbers of each component.

Abstract: The asymptotic behavior of expanding, generic, $T^2$-Symmetric, vacuum spacetimes is examined via numerical simulations. After validation of the numerical methods, the properties of these generic spacetimes are explored and compared to non-generic subfamilies where proven results exist. The non-generic subfamilies within this class, including the Kasner, the Gowdy, the pseudo-homogeneous, and the $B=0$ spacetimes, all have known asymptotic behaviors in the expanding direction which have been determined either from the explicit solutions or using analytic methods. For the $B\ne 0$ spacetimes, the generic case within the $T^2$-Symmetric vacuum solutions, the asymptotic behavior has not been determined analytically. In this work, we use numerical simulations to explore the asymptotic behavior of the $B\ne 0$ spacetimes. Our results indicate that, for these generic spacetimes, the asymptotic behavior in the expanding direction differs from that seen in the non-generic subfamilies. In addition to differences in asymptotic power laws, an apparent quasi-periodic exchange of energy from one gravitational mode to the other for the generic non-polarized solutions is observed.

Abstract: When gravitational waves pass by a massive object on its way to the Earth, strong gravitational lensing effect will happen. Thus the GW signal will be amplified, deflected, and delayed in time. Through analysing the lensed GW waveform, physical properties of the lens can be inferred. On the other hand, neglecting lensing effects in the analysis of GW data may induce systematic errors in the estimating of source parameters. As a space-borne GW detector, TianQin will be launched in the 2030s. It is expected to detect dozens of MBHBs merger as far as z = 15, and thus will have high probability to detect at least one lensed event during the mission lifetime. In this article, we discuss the capability of TianQin to detect lensed MBHBs signals. Three lens models are considered in this work: the point mass model, the SIS model, and the NFW model. The sensitive frequency band for space-borne GW detectors is around milli-hertz, and the corresponding GW wavelength could be comparable to the lens gravitational length scale, which requires us to account for wave diffraction effects. In calculating lensed waveforms, we adopt the approximation of geometric optics at high frequencies to accelerate computation, while precisely evaluate the diffraction integral at low frequencies. Through a Fisher analysis, we analyse the accuracy to estimate the lens parameters. We find that the accuracy can reach to the level of 10^-3 for the mass of point mass and SIS lens, and to the level of 10^-5 for the density of NFW lens. We also assess the impact on the accurate of estimating the source parameters, and find that the improvement of the accuracy is dominated by the increasing of SNR.

Abstract: We present analytical and numerical progress on black-hole binary spin precession at second post-Newtonian order using multi-timescale methods. In addition to the commonly used effective spin which acts as a constant of motion, we exploit the weighted spin difference and show that such reparametrization cures the coordinate singularity that affected the previous formulation for the case of equal-mass binaries. The dynamics on the precession timescale is written down in closed form in both coprecessing and inertial frames. Radiation-reaction can then be introduced in a quasi-adiabatic fashion such that, at least for binaries on quasi-circular orbits, gravitational inspirals reduce to solving a single ordinary differential equation. We provide a broad review of the resulting phenomenology and re-write the relevant physics in terms of the newly adopted parametrization. This includes the spin-orbit resonances, the up-down instability, spin propagation at past time infinity, and new precession estimators to be used in gravitational-wave astronomy. Our findings are implemented in version 2 of the public Python module PRECESSION. Performing a precession-averaged post-Newtonian evolution from/to arbitrarily large separation takes $\lesssim 0.1$ s on a single off-the-shelf processor. This allows for a wide variety of applications including propagating gravitational-wave posterior samples as well as population-synthesis predictions of astrophysical nature.

Abstract: We study the properties of spacelike singularities in spherically symmetric spacetimes obeying the Einstein equations, in the presence of matter. We consider in particular matter described by a scalar field, both in the presence of an electromagnetic field and without. We prove that if a spacelike singularity obeying several reasonable assumptions is formed, then the Hawking mass, the Kretschmann scalar, and the matter fields have inverse polynomial blow-up rates near the singularity that may be described precisely. Furthermore, one may view the resulting spacetime in the context of the BKL heuristics regarding space-like singularities in relativistic cosmology. In particular, near any point $p$ on the singular boundary in our spherically symmetric spacetime, we obtain a leading order BKL-type expansion, including a description of Kasner exponents associated to $p$. This provides a rigorous description of a detailed correspondence between Kasner-like singularities most often associated to the cosmological setting, and the singularities observed in (spherically symmetric) gravitational collapse. Moreover, we outline a program concerning the study of the stability and instability of spacelike singularities in the latter picture, both outside of spherical symmetry and within (where the electromagnetic field acts as a proxy for angular momentum) - in particular we signify the importance of cosmological phenomena including subcritical regimes and Kasner bounces in the collapse setting.