Related papers: Numerical evolutions of the linearised conformal E…
The linearisation of a second-order formulation of the conformal Einstein field equations (CEFEs) in Generalised Harmonic Gauge (GHG), with trace-free matter is derived. The linearised equations are obtained for a general background and…
In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's…
This is the second paper in a series describing a numerical implementation of the conformal Einstein equation. This paper deals with the technical details of the numerical code used to perform numerical time evolutions from a "minimal" set…
In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…
In this work, we study linearised gravitational fields on the entire Minkowski space-time including space-like infinity. The generalised conformal field equations linearised about a Minkowski background are utilised for this purpose. In…
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…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are…
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…
While the Teukolsky equation plays a central role in traditional treatments of perturbations of algebraically special spacetimes, its relation to Friedrich's conformal Einstein field equations (CEFEs) remains largely unexplored. Here we…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
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 thesis describes the application of numerical techniques to solve Einstein's field equations in three distinct cases. First we present the first long-term stable second order convergent Cauchy characteristic matching code in…
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…
In this paper we prove the nonlinear stability of Minkowski space-time with a translation Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein equations with a scalar field. We…
In this work we review the application of a functional method, serving as an alternative to the Wilsonian Exact Renormalization approach, to stringy bosonic $\sigma$-models with metric and dilaton backgrounds on a spherical world sheet [1].…
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…
In this article, it is shown how the extended conformal Einstein field equations and a gauge based on the properties of conformal geodesics can be used to analyse the non-linear stability of de Sitter-like spacetimes with spatial sections…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl…