Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes

Abstract

It is known that spherically symmetric static spacetimes admit a foliation by {\deg}at hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of {\deg}at foliations for studying black hole physics. Here {\deg}at spherically symmetric spacelike hy- persurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit {\deg}at spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the time- like Killing vector. This result guarantees the uniqueness of {\deg}at spherically symmetric foliations for such spacetimes.