Related papers: The initial value problem in numerical relativity
A general relativistic, stationary and axisymmetric black hole in a four-dimensional asymptotically-flat spacetime is fully determined by its mass, angular momentum and electric charge. The expectation that astrophysically relevant black…
This paper revisits the classical construction of initial data using the conformal method, as originally proposed by Holst, Nagy, and Tsogtgerel and later refined by Maxwell. We demonstrate that the existence of the solution can be proven…
The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic geometry. To do this, we use the parabolic partial differential equation for prescribing scalar…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
We study the local in time well-posedness of the initial boundary value problem (IBVP) for the vacuum Einstein equations in general relativity with geometric boundary conditions. For conformal-mean curvature boundary conditions, consisting…
We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…
(Abridged) By asymptotically matching a post-Newtonian (PN) metric to two tidally perturbed Schwarzschild metrics, we generate approximate initial data (in the form of a 4-metric) for a nonspinning black hole binary in a circular orbit. We…
A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to…
The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized…
We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision…
The characteristic initial value problem has been implemented as a robust computational algorithm (the PITT NULL CODE), with direct application to binary black holes. The event horizon can be analyzed by characteristic techniques as a…
We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
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 a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface…
The Einstein constraint equations have been the subject of study for more than fifty years. The introduction of the conformal method in the 1970's as a parameterization of initial data for the Einstein equations led to increased interest in…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…