Related papers: Initial Data for Numerical Relativity
We propose and explore a "stationary 1+log" slicing condition for the construction of solutions to Einstein's constraint equations. For stationary spacetimes, these initial data will give a stationary foliation when evolved with "moving…
Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…
The goal of this paper is to present the physics behind Brill initial data sets as an excellent tool for numerical experiments of axisymmetric spacetimes, data sets which are practical applications of HPC for numerical solutions of…
The focus of this work is on the construction of initial data including a neutron star on a hyperboloidal slice. As simplest scenario for this first step, spherical symmetry is considered together with a polytropic-like equation of state…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
Nonspherical perturbation theory has been necessary to understand the meaning of radiation in spacetimes generated through fully nonlinear numerical relativity. Recently, perturbation techniques have been found to be successful for the time…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
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…
Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through…
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
Within the isolated horizon formalism, we investigate a static axisymmetric space-time of a black hole influenced by matter in its neighborhood. To illustrate the role of ingredients and assumptions in this formalism, we first show how, in…
General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this…
We give a simple construction of smooth, asymptotically flat vacuum initial data modeling a relativistic collapsing $N$--body system, with independently prescribed ADM energy, linear momentum, and angular momentum for each component,…
Numerical-relativity (NR) simulations of compact binaries are expected to be an invaluable tool in gravitational-wave (GW) astronomy. The sensitivity of future detectors such as the Einstein Telescope (ET) will place much higher demands on…
Dynamical black holes in the non-perturbative regime are not mathematically well understood. Studying approximate symmetries of spacetimes describing dynamical black holes gives an insight into their structure. Utilising the property that…
We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and…
COCAL is a code for computing equilibriums or quasiequilibrium initial data of single or binary compact objects based on finite difference methods. We present the results of supplementary convergence tests of COCAL code using time symmetric…
The conformal method is a technique for finding Cauchy data in general relativity solving the Einstein constraint equations, and its parameters include a conformal class, a conformal momentum (as measured by a densitized lapse), and a mean…
We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal…