Séminaire de Physique ThéoriqueA fully-constrained formulation of Einstein equations: setup and numerical implementation
Jerome Novak (LUTH)
Thursday 26 January 2012 14:00 - Tours - Salle 1180 (Bât E2)
Numerical approaches to the solution of the Einstein field equations have now become quite efficient in obtaining approximate spacetimes. However, because of the covariance of the equations, it is very important to devise reliable and well-posed formulations of these equations, in order to have stable numerical integration. In this seminar, after an introduction to this field of numerical relativity and to the 3+1 approach to the Einstein equations, I shall present the so-called fully-constrained formulation, where the equations of general relativity are cast into a maximal number of elliptic-type partial differential equations, and only two hyperbolic ones, which can be related to the two polarization degrees of the gravitational waves. I shall then briefly present the numerical techniques we are using to solve these equations, before giving some details on the solution of the divergence-free wave equation for a symmetric rank-2 tensor, coming from the evolution of the spatial metric.