Related papers: Hyperbolicity of the BSSN system of Einstein evolu…
BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the conformal-traceless decomposition but keeping the three…
The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in…
We experiment with several new modifications for the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein field equations and demonstrate how these modifications affect the stability of numerical black hole evolution…
The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen…
Different formulations of Einstein's equations used in numerical relativity can affect not only the stability but also the accuracy of numerical simulations. In the original Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation, the loss of…
We prove that when the equations are restricted to the principal part the standard version of the BSSN formulation of the Einstein equations is equivalent to the NOR formulation for any gauge, and that the KST formulation is equivalent to…
We show that the Kidder-Scheel-Teukolsky family of hyperbolic formulations of the 3+1 evolution equations of general relativity remains hyperbolic when coupled to a recently proposed modified version of the Bona-Masso slicing condition.
The Einstein evolution equations have been written in a number of symmetric hyperbolic forms when the gauge fields--the densitized lapse and the shift--are taken to be fixed functions of the coordinates. Extended systems of evolution…
Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the…
We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a…
Following Brown, in this paper we give an overview of how to modify standard hyperbolic formulations of the 3+1 evolution equations of General Relativity in such a way that all auxiliary quantities are true tensors, thus allowing for these…
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…
We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry…
There is strong evidence indicating that the particular form used to recast the Einstein equation as a 3+1 set of evolution equations has a fundamental impact on the stability properties of numerical evolutions involving black holes and/or…
We study the dynamics of Einstein's equations in Ashtekar's variables from the point of view of the theory of hyperbolic systems of evolution equations. We extend previous results and show that by a suitable modification of the Hamiltonian…
We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used…
This paper is concerned exclusively with axisymmetric spacetimes. We want to develop reductions of Einstein's equations which are suitable for numerical evolutions. We first make a Kaluza-Klein type dimensional reduction followed by an ADM…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. In order to complete a long-term and accurate simulations of binary compact objects, people seek a robust set of equations against…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and…