Project: Apparent Horizon Boundary Conditions

P. Anninos, K. Camarda, G. Daues, J. Massó, E. Seidel, W.-M. Suen, P. Walker

Abstract

It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. Such a scheme is based on using (1) a horizon locking coordinate which locks the coordinate system to the geometry and (2) a finite differencing scheme which respects the causal structure of the spacetime. The horizon locking coordinate can be affected by a number of shift conditions, namely, a `distance freezing' shift, an `area freezing' shift, an `expansion freezing' shift, or the minimal distortion shift.

Progress Report

Our work on the 1D numerical evolutions is summarized in the preprint Horizon Boundary Condition for Black Hole Spacetimes.

Apparent horizon boundary conditions are now being implemented in 3D in the G Code . They are applied to both the case of one spherical black hole and that of the head-on collision of two black holes.

Related Projects

This project is closely related to the 3DBH project. For a description of the code that we use, see the G Code project. This project is also related to the Slicing/Shift Coordinate Conditions project, in which we study the choice and implementation of coordinate conditions in 3D Numerical Relativity.