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 to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.
|Original language||English (US)|
|Number of pages||16|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - Jan 1 1997|
ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)