General Relativity And Quantum Cosmology

In a previous paper (P. D. Mannheim, Phys. Rev. D 102, 123535 (2020)) we studied cosmological perturbation theory in the cosmology associated with the fourth-order derivative conformal gravity theory, and provided an exact solution to the theory in the recombination era. In this paper we present an exact solution that holds all the way from recombination until the current era.

A covariant, scalar-tensor gravity is constructed such that the static, spherically symmetric Rezzolla-Zhidenko metric is an exact solution to the theory. The equations describing gravitational perturbations of this spacetime, which represents a generic black hole possessing an arbitrary number of hairs, can then be derived. This allows for a self-consistent study of the associated quasinormal modes. It is shown that mode spectra are tied to not only the non-Einstein parameters in the metric but also to those that appear at the level of the action, and that different branches of the exact theory can, in some cases, predict significantly different oscillation frequencies and damping times. For choices which make the theory appear more like general relativity in some precise sense, we find that a nontrivial Rezzolla-Zhidenko parameter space is permissible under current constraints on fundamental ringdown modes observed by Advanced LIGO.

We show that there exist steady states of the massless Einstein-Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary number of shells, necessarily well separated, can surround the black hole. To our knowledge this is the first result of static self-gravitating solutions to any massless Einstein-matter system which surround a black hole. We also include a numerical investigation about the properties of the shells.

We study thermodynamics and critical behaviors of higher-dimensional Lovelock black holes with non-maximally symmetric horizons in the canonical ensemble of extended phase space. The effects from non-constancy of the horizon of the black hole via appearing two chargelike parameters in thermodynamic quantities of third-order Lovelock black holes are investigated. We find that Ricci flat black holes with nonconstant curvature horizon show critical behavior. This is an interesting feature that is not seen for any kind of black hole in Einstein or Lovelock gravity in the literature. We examine how various interesting thermodynamic phenomena such as standard first-order small-large black hole phase transition, a reentrant phase transition, or zeroth order phase transition happens for Ricci flat, spherical, or hyperbolic black holes with nonconstant curvature horizon depending on the values of Lovelock coefficient and chargelike parameters. While for a spherical black hole of third order Lovelock gravity with constant curvature horizon phase transition is observed only for 7?�d??1 , for our solution criticality and phase transition exist in every dimension. With a proper choice of the free parameters, a large-small-large black hole phase transition occurs. This process is accompanied by a finite jump of the Gibbs free energy referred to as a zeroth-order phase transition. For the case κ=?? a novel behavior is found for which three critical points could exist.

Numerical simulations of binary black holes are accompanied by an initial spurious burst of gravitational radiation (called `junk radiation') caused by a failure of the initial data to describe a snapshot of an inspiral that started at an infinite time in the past. A previous study showed that the superposed harmonic (SH) initial data gives rise to significantly smaller junk radiation. However, it is difficult to construct SH initial data for black holes with dimensionless spin ???.7 . We here provide a class of spatial coordinate transformations that extend SH to higher spin. The new spatial coordinate system, which we refer to as superposed modified harmonic (SMH), is characterized by a continuous parameter -- Kerr-Schild and harmonic spatial coordinates are only two special cases of this new gauge. We compare SMH with the superposed Kerr-Schild (SKS) initial data by evolving several binary black hole systems with ?=0.8 and 0.9 . We find that the new initial data still leads to less junk radiation and only small changes of black hole parameters (e.g. mass and spin). We also find that the volume-weighted constraint violations for the new initial data converge with resolution during the junk stage (t??00M) , which means there are fewer high-frequency components in waveforms at outer regions.

We study a false vacuum decay in a two-dimensional black hole spacetime background. The decay rate in the case that nucleation site locates at a black hole center has been calculated in the literature. We develop a method for calculating the decay rate of the false vacuum for a generic nucleation site. We find that the decay rate becomes larger when the nucleation site is close to the black hole horizon and coincides with that in Minkowski spacetime when the nucleation site goes to infinity.

Black-hole spacetimes are known to possess closed light rings. We here present a remarkably compact theorem which reveals the physically intriguing fact that these unique null circular geodesics provide the {\it fastest} way, as measured by asymptotic observers, to circle around spinning Kerr black holes.

Modifying gravity at large distances by means of a massive graviton may explain the observed acceleration of the Universe without Dark Energy. The standard paradigm for Massive Gravity is the Fierz-Pauli theory, which, nonetheless, displays well known flaws in its massless limit. The most serious one is represented by the vDVZ discontinuity, which consists in a disagreement between the massless limit of the Fierz-Pauli theory and General Relativity. Our approach is based on a field theoretical treatment of Massive Gravity: General Relativity, in the weak field approximation, is treated as a gauge theory of a symmetric rank-2 tensor field. This leads us to propose an alternative theory of linearized Massive Gravity, describing five degrees of freedom of the graviton, with a good massless limit, without vDVZ discontinuity, and depending on one mass parameter only, in agreement with the Fierz-Pauli theory.

The destructive interference of the neighbouring field configurations with infinite classical action in the gravitational path integral approach serves as a dynamical mechanism resolving the black hole singularity problem. It also provides an isotropic and homogeneous early universe without the need of inflation. In this work, we elaborate on the finite action in the framework of Horava-Lifshitz gravity -- a ghost-free QFT. Assuming the mixmaster chaotic solutions in the projectable H-L theory, we show that the beginning of the universe is homogeneous and isotropic. Furthermore, we show that the H-L gravity action selects only the regular black-hole spacetimes. We also comment on possibility of traversable wormholes in theories with higher curvature invariants.

We present the first searches for gravitational waves from r-modes of the Crab pulsar, coherently and separately integrating data from three stretches of the first two observing runs of Advanced LIGO using the F-statistic. The second run was divided in two by a glitch of the pulsar roughly halfway through. The frequencies and derivatives searched were based on radio measurements of the pulsar's spin-down parameters as described in Caride et al., Phys. Rev. D 100, 064013 (2019). We did not find any evidence of gravitational waves. Our best 90% confidence upper limits on gravitational wave intrinsic strain were 1.5e-25 for the first run, 1.3e-25 for the first stretch of the second run, and 1.1e-25 for the second stretch of the second run. These are the first upper limits on gravitational waves from r-modes of a known pulsar to beat its spin-down limit, and they do so by more than an order of magnitude in amplitude or two orders of magnitude in luminosity.