Related papers: Numerical Cauchy evolution of asymptotically AdS s…
We present the first proof-of-principle Cauchy evolutions of asymptotically global AdS spacetimes with no imposed symmetries, employing a numerical scheme based on the generalized harmonic form of the Einstein equations. In this scheme, the…
Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which can be…
We present a new hybrid Cauchy-characteristic evolution method that is particularly suited for the study of gravitational collapse in spherically-symmetric asymptotically (global) Anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows…
This thesis describes the application of numerical techniques to solve Einstein's field equations in three distinct cases. First we present the first long-term stable second order convergent Cauchy characteristic matching code in…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. We prove that the Schwarzschild-AdS spacetimes (the…
In this paper, we study the evolution of asymptotically AdS initial data for the spherically symmetric Einstein--massless Vlasov system for $\Lambda<0$, with reflecting boundary conditions imposed on timelike infinity $\mathcal{I}$, in the…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D…
Motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS spacetimes, we initiate the study of massive scalar waves satisfying $\Box_g \psi - \mu \psi =0$ on the interior of Anti-de Sitter (AdS) black holes. We prescribe…
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative…
We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with…
In this thesis the universal collapse of vacuum Brill waves is demonstrated numerically and analytically. This thesis presents the mathematical and numerical methods necessary to regularise and evolve Brill Gravitational Waves in spherical…
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations…
We prove the nonlinear stability of the cosmological region of Kerr de Sitter spacetimes. More precisely, we show that solutions to the Einstein vacuum equations with positive cosmological constant arising from data on a cylinder that is…
We present the first results for Cauchy nonlinear evolution of 3D, nonaxisymmetric distorted black holes. We focus on the extraction and verification of 3D waveforms determined by numerical relativity. We show that the black hole evolution…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
We show that $3$-dimensional AdS spacetime can be semiclassically unstable due to strongly interacting quantum field effects. In our previous paper, we have pointed out the possibility of such an instability of AdS$_3$ by inspecting linear…
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the…
Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…
In this paper, the connection between the Lorentz-covariant counterterms that regularize the four-dimensional AdS gravity action and topological invariants is explored. It is shown that demanding the spacetime to have a negative constant…