相关论文: Numerical treatment of the hyperboloidal initial v…

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…

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…

We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…

Some issues in the numerical treatment of the conformal field equations are discussed. In particular, the problem of obtaining smooth initial data for the hyperboloidal initial value problem is described and solution methods are presented.

The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages…

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…

Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…

We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field…

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…

The spinorial version of the conformal vacuum Einstein field equations are used to construct a system of quasilinear wave equations for the various conformal fields. As a part of the analysis we also show how to construct a subsidiary…

To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…

This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…

We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the…

We derive, in 3+1 spacetime dimensions, two alternative systems of quasi-linear wave equations, based on Friedrich's conformal field equations. We analyse their equivalence to Einstein's vacuum field equations when appropriate constraint…

We make use of an improved existence result for the characteristic initial value problem for the conformal Einstein equations to show that given initial data on two null hypersurfaces $\mathcal{N}_\star$ and $\mathcal{N}'_\star$ such that…

We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are…

We use numerical integration to solve the field equations of conformal gravity, assuming a metric that is static and spherically symmetric. Our solution is an extension of that found by Mannheim and Kazanas; it indicates, as expected, that…

This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at AEI in the last years, and discuss a…

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…

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…