General spherically symmetric constant mean curvature foliations of the Schwarzschild solution

Journal Article · Wed Jul 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.024017· OSTI ID:21316240

Malec, Edward; Murchadha, Niall O ^[1]

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1. Physics Department, Jagiellonian University, Krakow (Poland)

We consider a family of spherical three-dimensional spacelike slices embedded in the Schwarzschild solution. The mean curvature is constant on each slice but can change from slice to slice. We give a simple expression for an everywhere positive lapse and thus we show how to construct foliations. There is a barrier preventing the mean curvature from becoming large, and we show how to avoid this so as to construct a foliation where the mean curvature runs all the way from zero to infinity. No foliation exists where the mean curvature goes from minus to plus infinity. There are slicings, however, where each slice passes through the bifurcation sphere R=2M and the lapse only vanishes at this one point, and is positive everywhere else, while the mean curvature does run from minus to plus infinity. Symmetric foliations of the extended Schwarzschild spacetime degenerate at a critical point, where we show that the lapse function exponentially approaches zero.

• OSTI ID: 21316240
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BIFURCATION
SCHWARZSCHILD METRIC
SPACE-TIME
SPHERICAL CONFIGURATION
SYMMETRY
THREE-DIMENSIONAL CALCULATIONS