Related papers: Advanced General Relativity Notes
Exact solutions describing rotating black holes can offer important tests for alternative theories of gravity, motivated by the dark energy and dark matter problems. We present an analytic rotating black hole solution for a class of…
Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this paper, we show that the black-hole solutions of these theories…
The description of a point mass in general relativity (GR) is given in the framework of the field formulation of GR where all the dynamical fields, including the gravitational field, are considered in a fixed background spacetime. With the…
This doctoral thesis is organized into seven chapters. The first chapter introduces readers to the formation of black holes and naked singularities as an end state of continuous gravitational collapse. The physical and geometrical…
A general Hamiltonian approach to black hole thermodynamics is used to study entropy and conserved charges for Kerr-AdS solutions in general relativity. These thermodynamic variables are first consistently defined by choosing suitable…
An introduction to generalized thermodynamics of quantum black holes, in the one-loop approximation, is given. The material is aimed at graduate students. The topics include: quantum evaporation of black holes, Euclidean formulation of…
The strategy of obtaining the familiar Kerr-Newman solution in general relativity is based on either using the metric ansatz in the Kerr-Schild form, or applying the method of complex coordinate transformation to a non-rotating charged…
These notes introduce basic aspects of black hole thermodynamics. I review the classical laws of black hole mechanics, give a brief introduction to the essential concepts of quantum field theory in curved spacetime, and derive the Unruh and…
Black holes are an ubiquitous end state of stellar evolution and successfully explain some of the most extreme physics encountered in astronomical observations. The Kerr geometry is the known exact solution to Einstein's equations for a…
I present an elementary primer of black hole physics, including its general relativity basis, all peppered with astrophysical illustrations. Following a brief review of the process stellar collapse to a black hole, I discuss the…
We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes…
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret…
We study two large classes of alternative theories, modifying the action through algebraic, quadratic curvature invariants coupled to scalar fields. We find one class that admits solutions that solve the vacuum Einstein equations and…
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…
Observations of the black hole shadow of supermassive black holes, such as Sagittarius A* at the center of our Milky Way galaxy, allow us to study the properties of black holes and the nature of strong-field gravity. According to the Kerr…
The null geodesics that describe photon orbits in the spacetime of a rotating electrically charged black hole (Kerr-Newman) are solved exactly including the contribution from the cosmological constant. We derive elegant closed form…
The observation of gravitational waves has inaugurated a new era for testing gravitational theories in strong-field, nonlinear regimes. Gravitational waves emit during the ringdown phase of binary black hole mergers and from extreme mass…
A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the…
We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that…
These lectures notes contain an introduction to General Relativity. They are addressed to a general mathematical audience with no specific background in physics. The goal is to motivate and explain Einstein's theory of gravity and discuss…