Related papers: Boundary Conditions for the Gravitational Field
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…
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…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
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 strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld…
In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the…
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this…
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…
An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic…
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…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new…
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of…
We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…
This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further…
New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike…
In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…