Related papers: Approximate Solutions to the Binary Black Hole Ini…
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 solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild…
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…
We explore whether a new method to solve the constraints of Einstein's equations, which does not involve elliptic equations, can be applied to provide initial data for black holes. We show that this method can be successfully applied to a…
A black hole solution of Einstein's field equations with cylindrical symmetry is found. Using the Hamiltonian formulation one is able to define mass and angular momentum for the cylindrical black hole through the corresponding and…
Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to…
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 construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent…
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…
An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…
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…
An intriguing open problem in general relativity is whether a stationary equilibrium configuration of multiple, physically relevant black holes can exist. In such a hypothetical setup, the gravitational attraction would need to be balanced…
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…
Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that…
We study the momentum and Hamiltonian constraints of vacuum Einstein equations, within the Bowen-York formalism, for two interacting black holes in close separation, with anti-parallel spins and anti-parallel linear momenta. We give an…
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…
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 analytically solve the constraints in General Relativity for two black holes with arbitrary momenta and spin up to third order in these parameters. We compute the location and geometry of the apparent horizon, which depend on the spins,…
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 a new approach to the problem of binary black holes in the pre-coalescence stage, i.e. when the notion of orbit has still some meaning. Contrary to previous numerical treatments which are based on the initial value formulation of…