Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-03-27
Phys.Rev.D80:024017,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
2 new figures, new references, 8 pages. Matches the version accepted by the Physical Review D
Scientific paper
10.1103/PhysRevD.80.024017
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.
Malec Edward
O'Murchadha Niall
No associations
LandOfFree
The general spherically symmetric constant mean curvature foliations of the Schwarzschild solution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The general spherically symmetric constant mean curvature foliations of the Schwarzschild solution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The general spherically symmetric constant mean curvature foliations of the Schwarzschild solution will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-21450