General Relativity and Quantum Cosmology (gr-qc)

Abstract: This paper investigates the quasinormal mode (QNM) vibrations of a rotating cylindrical black hole (or black string) spacetime that is surrounded by a thin shell rotating synchronously with the black string's axis. The existence of the thin shell leads to a piecewise metric of the black hole spacetime beyond the horizon, which is divided into two stationary spacetime parts by the radius of the thin shell. As a result, the potential function $V(r)$ of the QNM equation is also discontinuous. To solve the QNM equation with the discontinuous potential function, we propose two methods, matrix method and generalized Horowitz-Hubeny Method. We find that the influence of the thin shell can reduce the QNM frequency of the black string while alleviating their amplitude decay rate. Our suggested method can be easily applied to other QNM calculations of black hole spacetime with discontinuous potential function, thus facilitating investigations into more intricate and realistic black hole spacetimes, such as those with accretion disks. Additionally, the finite difference method is employed to investigate the spacetime too. This analysis discloses a substantial gap in the potential function when the thin shell's mass and charge achieve sufficiently high values, resulting in the outer spacetime nearing gravitational collapse and extreme black hole scenarios. Within this gap, the QNM wave displays oscillations, producing an echo effect. Moreover, it is established that the closeness of the spacetime to the collapse threshold and charge extremality have positive correlation with the beat interval of this echo.

Abstract: Metric perturbations in General Relativity are usually separated into three distinct classes: scalar, vector, and tensor. In many cases these modes are separable, i.e. they satisfy independent equations of motion for each mode. However, in the present paper we argue that in many cases tensor and scalar modes are not separable, no matter what gauge conditions are chosen. The propagation of any of these mode depends on the other. A realistic example providing such mixing is presented.

Abstract: Weyl's conformal gravity theory, which is considered as a compelling alternative to general relativity theory, has been claimed to describe the observed flat rotation curve feature of spiral galaxies without the need of invoking dark matter. However, it is important to examine whether the Weyl theory can also explain the relevant gravitational lensing observations correctly without considering any dark matter. In this regard, the gravitational bending angle in static spherically space-time (Mannheim-Kazanas metric) in Weyl theory has been calculated by several authors over the last two decades, but the results are found largely divergent. In this work, we have revisited the problem and obtain the correct and consistent expression of the deflection angle in conformal gravity. Subsequently we perform the gravitational lensing analysis. We compare the prediction of Weyl gravity with the gravitational lensing observations of the rich galaxy clusters Abell 370 and Abell 2390 and is found that Weyl theory cannot describe the stated lensing observations without considering dark matter.

Abstract: This paper reviews the role of black holes in the context of fundamental physics. After recalling some basic results stemming from Planckian string calculations, I present three examples of how stringy effects can improve the curvature singularity of classical black hole geometries.

Abstract: Smooth Cauchy data for the Einstein-Lambda-vacuum field equations with positive cosmological constant Lambda that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary Scri+ in its future. The conformal Einstein equations determine a smooth conformal extension across Scr+ that defines on `the other side' again a Lambda-vacuum solution. In this article we discuss to what extent these properties generalize to the future asymptotic behaviour of solutions to the Einstein-Lambda equations with matter. We study FLRW solutions and the Einstein-Lambda equations coupled to conformally covariant matter transport equations, to conformally privileged matter equations, and to conformally non-covariant matter equations. We present recent results on the Einstein-Lambda-perfect-fluid equations with a non-linear asymptotic dust or asymptotic radiation equation of state.

Abstract: The first-order thermodynamics of scalar-tensor theory is a novel approach that exploits the intriguing relationship between gravity and thermodynamics to better understand the space of gravity theories. It is based on using Eckart's first-order irreversible thermodynamics on the effective imperfect fluid describing scalar-tensor gravity and characterises General Relativity as an equilibrium state, and scalar-tensor theories as non-equilibrium states, naturally describing the approach to equilibrium. Applications of this framework to cosmology, extensions to different classes of modified theories, and the formulation of two complementary descriptions based on the notions of temperature and chemical potential all contribute to a new and unifying picture of the landscape of gravity theories.

Abstract: We study spherical collapse of a scalar cloud in scalar-Gauss-Bonnet gravity - a theory in which black holes can develop scalar hair if they are in a certain mass range. We show that an additional quadratic coupling of the scalar field to the Ricci scalar can mitigate loss of hyperbolicity problems that have plagued previous numerical collapse studies and instead lead to well-posed evolution. This suggests that including specific additional interactions can be a successful strategy for tackling well-posedness problems in effective field theories of gravity with nonminimally coupled scalars. Our simulations also show that spherical collapse leads to black holes with scalar hair when their mass is below a mass threshold and above a minimum mass bound and that above the mass threshold the collapse leads to black holes without hair, in line with results in the static case and perturbative analyses. For masses below the minimum mass bound we find that the scalar cloud smoothly dissipates, leaving behind flat space.