Related papers: Approximate Analytical Solutions to the Initial Da…
We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily…
We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two…
Standard puncture initial data have been widely used for numerical binary black hole evolutions despite their shortcomings, most notably the inherent lack of gravitational radiation at the initial time that is later followed by a burst of…
We construct initial data suitable for the Kerr stability conjecture, that is, solutions to the constraint equations on a spacelike hypersurface with boundary entering the black hole horizon that are arbitrarily decaying perturbations of a…
A benchmark problem for numerical relativity has been the head-on collision of two black holes starting from the ``Misner initial data,'' a closed form momentarily stationary solution to the constraint equations with an adjustable closeness…
Numerical relativity, applied to collisions of black holes, starts with initial data for black holes already in each other's strong field. The initial hypersurface data typically used for computation is based on mathematical simplifying…
In numerical evolutions of binary black holes (BBH) it is desirable to easily control the orbital eccentricity of the BBH, and the number of orbits completed by the binary through merger. This paper presents fitting formulae that allow to…
Numerical relativity simulations provide a means by which to study the evolution and end point of strong over-densities in cosmological spacetimes. Specific applications include studies of primordial black hole formation and the robustness…
We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic…
We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal…
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…
The construction of constraint-satisfying initial data is an essential element for the numerical exploration of the dynamics of compact-object binaries. While several codes have been developed over the years to compute generic…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
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…
We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a…
In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface…
When numerically solving Einstein's equations for binary black holes (BBH), we must find initial data on a three-dimensional spatial slice by solving constraint equations. The construction of initial data is a multi-step process, in which…
We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these…
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 construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in…