相关论文: Numerical construction of initial data sets of bin…
We present a novel implicit numerical implementation of the parabolic-hyperbolic formulation of the constraints of general relativity. The proposed method is unconditionally stable, has the advantage of not requiring the imposition of any…
Near-Kerr black hole initial datasets are constructed by applying either the parabolic-hyperbolic or the algebraic-hyperbolic form of the constraints. In both cases, strongly and weakly asymptotically flat initial datasets with desirable…
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 $4^{th}$…
In this paper we consider the hyperbolic formulation of the constraints introduced by R\'acz. Using the numerical framework recently developed by us we construct initial data sets which can be interpreted as nonlinear perturbations of…
Two new methods have been proposed for solving the gravitational constraints without using elliptic solvers by formulating them as either an algebraic-hyperbolic or parabolic-hyperbolic system. Here, we compare these two methods and present…
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…
In this paper we continue earlier investigations of evolutionary formulations of the Einstein vacuum constraint equations originally introduced by R\'{a}cz. Motivated by the strong evidence from these works that the resulting vacuum initial…
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…
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…
In this paper, we continue our investigations of R\'acz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which…
Systematic numerical investigations of the asymptotics of near Schwarzschild vacuum initial data sets is carried out by inspecting solutions to the parabolic-hyperbolic and to the algebraic-hyperbolic forms of the constraints, respectively.…
By applying a parabolic-hyperbolic formulation of the constraints and superposing Kerr-Schild black holes, a simple method is introduced to initialize time evolution of binary systems. As the input parameters are essentially the same as…
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…
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…
Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the Spectral Einstein Code, to allow robust…
The construction of initial data for black-hole binaries usually involves the choice of free parameters that define the spins of the black holes and essentially the eccentricity of the orbit. Such parameters must be chosen carefully to…
We construct a family of asymptotically flat Cauchy initial data for the Einstein vacuum equations that contain no trapped surfaces, yet whose future development admits multiple causally independent trapped surfaces. Assuming the weak…
An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to…
We present a new numerical scheme to solve the initial value problem for black hole-neutron star binaries. This method takes advantage of the flexibility and fast convergence of a multidomain spectral representation of the initial data to…