Related papers: Finite difference schemes for second order systems…
We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasi-linear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between.…
Keeping Einstein's equations in second order form can be appealing for computational efficiency, because of the reduced number of variables and constraints. Stability issues emerge, however, which are not present in first order…
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…
We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the…
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…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
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…
Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second order symmetric hyperbolic. It is discretized in four-dimensional spacetime by Finite Differences, Finite Elements, and Interior…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
The Einstein's linear equation of a small perturbation in a space-time with a homogeneous section of low dimension, is studied. For every harmonic mode of the horizon, there are two solutions which behave differently at large distance $r$.…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein…
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…
We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper (hep-th/0305147) to a charged black hole background whose horizon is described by an…
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…
It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. In this paper we report on the details of the implementation of this…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
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…