Related papers: Initial Data for Numerical Relativity
This article is concerned with the derivation of the Gauss-Codazzi's constraints equations on the initial light cone for geometric transport equations in general relativity. Temporal-gauge-dependent constraints are addressed too and…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems…
In this article, we revisit the initial data rigidity theorem of Eichmair, Galloway and Mendes (arxiv:2009.09527). The goal is to strengthen their result by showing that the initial data sets concerned carry a vector field that is lightlike…
A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each…
We present the first results from a new method for computing spacetimes representing corotating binary black holes in circular orbits. The method is based on the assumption of exact equilibrium. It uses the standard 3+1 decomposition of…
Towards the investigation of the full dynamics in higher-dimensional and/or stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show $(N+1)$-dimensional version of the ADM…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The…
We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is…
Using a constrained formalism for Einstein equations in Dirac gauge, we propose to compute excised quasistationary initial data for black hole spacetimes in full general relativity. Vacuum spacetime settings are numerically constructed by…
We present a basics of the Einstein General Theory of Relativity. In the first part of this review we derive relations of Riemann geometry which are used in the General Relativity. In the second part we discuss Einstein Equations and some…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
We construct initial data suitable for the Kerr stability conjecture, that is, solutions to the constraint equations on a spacelike hypersurface with boundary entering the black hole horizon that are arbitrarily decaying perturbations of a…
We study the method for generating the initial data of black hole systems in Gauss-Bonnet (GB) gravity. The initial data are assumed to be momentarily static and conformally flat. Although the equation for the conformal factor is highly…
We revisit the construction of maximal initial data on compact manifolds in vacuum with positive cosmological constant via the conformal method. We discuss, extend and apply recent results of Hebey et al. [19] and Premoselli [31] which…
We analyze Killing Initial Data on Cauchy surfaces in conformally rescaled vacuum space-times satisfying Friedrich's conformal field equations. As an application, we derive the KID equations on a spacelike $\mathcal{J}^-$.
Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, we show how the framework of numerical relativity can be used for studying cosmological…
Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the…