Related papers: Solving the Hamiltonian constraint for 1+log trump…
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…
We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R^3 for the nonsingular part of the metric conformal factor. With this approach we can…
We propose a new approach, based on the puncture method, to construct black hole initial data in the so-called trumpet geometry, i.e. on slices that asymptote to a limiting surface of non-zero areal radius. Our approach is easy to implement…
We revisit the construction of puncture black hole initial data in the conformal thin-sandwich decomposition of Einstein's constraint equations. It has been shown previously that this approach cannot yield quasiequilibrium wormhole data,…
The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are…
We describe a procedure for constructing initial data for boosted black holes in the moving-punctures approach to numerical relativity that endows the initial time slice from the outset with trumpet geometry within the black hole interiors.…
With the puncture method for black hole simulations, the second infinity of a wormhole geometry is compactified to a single "puncture point" on the computational grid. The region surrounding the puncture quickly evolves to a trumpet…
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…
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 calculate puncture initial data, corresponding to single and binary black holes with linear momenta, which solve the constraint equations of D dimensional vacuum gravity. The data are generated by a modification of the pseudo-spectral…
Black hole initial data is usually produced using Bowen-York type puncture initial data or by applying an excision boundary condition. The benefits of the Bowen-York initial data are the ability to specify the spin and momentum of the…
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 consider the initial data problem for several black holes in vacuum with arbitrary momenta and spins on a three space with punctures. We compactify the internal asymptotically flat regions to obtain a computational domain without inner…
We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices which extend to future null infinity. We solve this initial value problem numerically for several cases, including unequal mass binary black…
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the…
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 $4^{th}$…
The strong-field region inside a black hole needs special attention during numerical simulation. One approach for handling the problem is the moving puncture method, which has become an important tool in numerical relativity since it allows…
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…
While numerous numerical relativity simulations adopt a 1+log slicing condition, shock-avoiding slicing conditions form a viable and sometimes advantageous alternative. Despite both conditions satisfying similar equations, recent numerical…
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…