The Constant-Mean-Curvature Slicing of the Schwarzschild-de Sitter Space-Time

Abstract

Numerical simulations are important not only for gravitational collapse and formation of neutron stars and black holes but also for the purpose of investigating the highly inhomogeneous stage of our universe. In particular, the ‘cosmic no hair conjecture’ connected with the inflationary scenario is one of the issues which should be examined by numerical simulations. For the numerical simulations, the coordinate condition is crucial to investigate the physically important region of a space-time. It is well known that the constant-mean-curvature(CMC) time slicing coordinate is useful for the asymptotically flat space-time. However, in order to investigate cosmological problems, we would like to know the applicability of that coordinate for the asymptotically non-flat space-time. As for inhomogeneous space-time with an asymptotically de Sitter space, the Schwarzschild-de Sitter solution is known. We investigate how the CMC hypersurfaces foliate the Schwarzschild-de Sitter space-time.