Related papers: Boundary Conditions for the Gravitational Field
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…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…
We discuss the initial-boundary value problem of General Relativity. Previous considerations for a toy model problem in electrodynamics motivate the introduction of a variational principle for the lapse with several attractive properties.…
In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations…
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein…
The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free…
We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.