Related papers: Hyperboloidal evolution of test fields in three sp…
We discuss a gauge choice which allows us to avoid the introduction of artificial timelike outer boundaries in numerical studies of test fields based on a 3+1 decomposition of asymptotically flat background spacetimes. The main idea is to…
We show how to solve hyperbolic equations numerically on unbounded domains by compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate…
We present new results from two open source codes, using finite differencing and pseudo-spectral methods for the wave equations in (3+1) dimensions. We use a hyperboloidal transformation which allows direct access to null infinity and…
We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which…
We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…
This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free…
A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed…
We consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
The Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
The use of compactified hyperboloidal coordinates for metric formulations of the Einstein field Equations introduces formally singular terms in the equations of motion whose numerical treatment requires care. In this paper we study a…
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…
In this paper, we establish the global existence of a semi-linear class of hyperbolic equations in 3+1 dimensions, that satisfy the bounded weak null condition. We propose a conformal compactification of the future directed null-cone in…