Related papers: Advanced Lectures on General Relativity
General relativity in the form where gravitational perturbations together with other physical fields propagate on an auxiliary background is considered. With using the Katz-Bi{\v{c}}\'ak-Lynden-Bell technique new conserved currents,…
Three-dimensional spacetime with a negative cosmological constant has proven to be a remarkably fertile ground for the study of gravity and higher spin fields. The theory is topological and, since there are no propagating field degrees of…
Generalizations of the Schwarzschild and Kerr black holes are discussed in an astrophysically viable generalized theory of gravity, which includes higher curvature corrections in the form of the Gauss-Bonnet term, coupled to a dilaton. The…
The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I will go through the physics of the different phases…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of…
The goal of these lectures is to introduce readers with a basic knowledge of undergraduate physics (specifically non-relativistic quantum mechanics, special relativity, and electromagnetism) to the `current theory of everything': the…
This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and…
In this paper, we focus on massive Einstein-dilaton gravity including the coupling of dilaton scalar field to massive graviton terms, and then derive static and spherically symmetric solutions of charged dilatonic black holes in four…
We review selected recent results concerning the global structure of solutions of the vacuum Einstein equations. The topics covered include quasi-local mass, strong cosmic censorship, non-linear stability, new constructions of solutions of…
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
The text is an essentially self-contained introduction to four-dimensional N=1 supergravity, including its couplings to super Yang-Mills and chiral matter multiplets, for readers with basic knowledge of standard gauge theories and general…
These notes are a transcript of lectures given by the author in the XVIII Modave summer school in mathematical physics. The introduction is devoted to a detailed review of the literature on asymptotic symmetries, flat holography, and the…
In this work, we investigate the $n$-dimensional charged static black hole solutions in the Einstein-\ae ther theory. By taking the metric parameter $k$ to be $1,0$, and $-1$, we obtain the spherical, planar, and hyperbolic spacetimes…
We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…
Nerd abstract: Observational constraints on spacetime are reviewed, focusing on how the underlying physics (dark matter, dark energy, gravity) can be tested rather than assumed. Popular abstract: Space is not a boring static stage on which…
With the aim of continuing the exploration of near-horizon charges in higher-curvature gravity, searching for sectors leading to universal behaviors, we first provide a thorough revision and formulae of the covariant phase-space method…
Black hole thermodynamics of the Kerr-AdS spacetime in three-dimensional general relativity is analyzed using a Hamiltonian approach. The values of the conserved charges and entropy, obtained by a proper treatment of the AdS asymptotic…
This talk gives an overview of the recently-formulated Fluid/Gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in…
We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we…