Related papers: Numerical initial data deformation exploiting a gl…
Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically…
We discuss the initial value problem of general relativity in its recently unified Lagrangian and Hamiltonian pictures and present a multi-domain pseudo-spectral collocation method to solve the resulting coupled nonlinear partial…
We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
We show how to assign initial data for the characteristic Einstein-Yang-Mills-Higgs system on two intersecting smooth null hypersurfaces. We successfully adapt the hierarchical method set up by A. D. Rendall to solve the same problem for…
We present improved post-Newtonian-inspired initial data for non-spinning black-hole binaries, suitable for numerical evolution with punctures. We revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P. Diener, Phys.…
This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York,…
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from…
We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision…
We present an approximate metric for a binary black hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed…
Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…
The parabolic-hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$…
We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant…
We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood…
We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying the time-rotation ($t$-$\phi$) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that 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…
A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
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…
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…