Related papers: Numerical relativity with the conformal field equa…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
The conformal Einstein equations for a tracefree (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de…
The computations of numerical relativity make use of (3+1)- decompositions of Einstein field equations. We examine the conceptual characteristics of this method; instances of compact-star binaries are considered. The preeminent role of the…
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 first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and…
Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data.…
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…
The late stage of the inspiral of two black holes may have important non-Newtonian effects that are unrelated to radiation reaction. To understand these effects we approximate a slowly inspiralling binary by a stationary solution to…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure $p$, the spatial part $\underline{u} \in \R^3$ of the dimensionless four-velocity and the particle density $n$. Radially symmetric solutions of…
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 review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…
A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of…
We present a uniform (and unambiguous) procedure for scaling the matter fields in implementing the conformal method to parameterize and construct solutions of Einstein constraint equations with coupled matter sources. The approach is based…
Einstein's field equation of General Relativity (GR) has been known for over 100 years, yet it remains challenging to solve analytically in strongly relativistic regimes, particularly where there is a lack of a priori symmetry. Numerical…
We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater…
In this article we find the general, exact solution for the gravitational field equations for diagonal, vacuum, separable metrics. These are metrics each of whose terms can be separated into functions of each space-time variable separately.…