Related papers: Towards absorbing outer boundaries in General Rela…
In a recent article, we constructed a hierarchy B_L of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a…
We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include…
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…
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…
Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
Errors due to imperfect boundary conditions in numerical relativity simulations of binary black holes can produce unphysical reflections of gravitational waves which compromise the accuracy of waveform predictions, especially for…
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 late stage of the inspiral of two black holes may have important non-Newtonian effects that are unrelated to radiation reaction. To understand these effects we approximate a slowly inspiralling binary by a stationary solution to…
Recently, there has been much interest in black hole echoes, based on the idea that there may be some mechanism (e.g., from quantum gravity) that waves/fields falling into a black hole could partially reflect off of an interface before…
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
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 present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…
The evolution of black holes in "confining boxes" is interesting for a number of reasons, particularly because it mimics the global structure of Anti-de Sitter geometries. These are non-globally hyperbolic space-times and the Cauchy problem…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
With the goal of bringing theory, particularly numerical relativity, to bear on an astrophysical problem of critical interest to gravitational wave observers we introduce a model for coalescence radiation from binary black hole systems. We…
It is straightforward to take the gravitational wave solution to first order in $v/c$ far from a binary source in a Minkowski background and adapt it to the Friedmann-Lemaitre-Robertson-Walker (FLRW) background, representing an expanding…
We investigate the interaction between a non-rotating black hole and incoming gravitational waves using the characteristic formulation of the Einstein field equations, framed as a Bondi problem. By adopting retarded time as the null…