Related papers: Excision boundary conditions for the conformal met…
We define and extensively test a set of boundary conditions that can be applied at black hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism.…
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 construct new models of black hole-neutron star binaries in quasiequilibrium circular orbits by solving Einstein's constraint equations in the conformal thin-sandwich decomposition together with the relativistic equations 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…
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…
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…
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
In relation to the BSSN formulation of the Einstein equations, we write down the boundary conditions that result from the vanishing of the projection of the Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up a…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
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 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…
We make use of the metric version of the conformal Einstein field equations to construct anti-de Sitter-like spacetimes by means of a suitably posed initial-boundary value problem. The evolution system associated to this initial-boundary…
This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the…
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…
Using a metric conformal formulation of the Einstein equations, we develop a construction of 4-dimensional anti-de Sitter-like spacetimes coupled to tracefree matter models. Our strategy relies on the formulation of an initial-boundary…
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…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…