1306.5976 (Isabel Cordero-Carrión et al.)

An excision scheme for black holes in constrained evolution
formulations: spherically symmetric case    [PDF]

Isabel Cordero-Carrión, Nicolas Vasset, Jérôme Novak, José Luis Jaramillo

Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead appropriate boundary conditions at the excised surface. In this work we present recent developments of this technique in the case of constrained formulations of Einstein equations and for spherically symmetric spacetimes. We present a new set of boundary conditions to apply to the elliptic system in the fully-constrained formalism of Bonazzola et al. (2004), at an arbitrary sphere inside the apparent horizon. Analytical properties of this system of boundary conditions are studied and, under some assumptions, an exponential convergence toward the stationary solution is exhibited for the vacuum spacetime. This is verified in numerical examples, together with the applicability in the case of the accretion of a scalar field onto a Schwarzschild black hole.

View original: http://arxiv.org/abs/1306.5976