相关论文: Black hole initial data by numerical integration o…

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…

In this paper we investigate the parabolic-hyperbolic formulation of the vacuum constraint equations introduced by R{\'a}cz with a view to constructing multiple black hole initial data sets without spin. In order to respect the natural…

The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic and extrinsic geometry. To do this, we use the parabolic partial differential equation for…

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…

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…

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…

We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a…

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.…

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…

When using the black hole exclusion (horizon boundary condition) technique, $K$ is usually nonzero and spatially variable, so none of the special cases of York's conformal-decomposition algorithm apply, and the full 4-vector nonlinear York…

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…

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…

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…

Numerical relativity codes now being developed will evolve initial data representing colliding black holes at a relatively late stage in the collision. The choice of initial data used for code development has been made on the basis of…

The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic geometry. To do this, we use the parabolic partial differential equation for prescribing scalar…

The damped harmonic gauge is important for numerical relativity computations based on the generalized harmonic formulation of Einstein's equations, and is used to reduce coordinate distortions near binary black hole mergers. However,…

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…

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 review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry.…

Initial data for boosted Kerr black hole are constructed in an axially symmetric case. Momentum and hamiltonian constraints are solved numerically using finite element method (FEM) algorithms. Both Bowen-York and puncture boundary…