What does Birkhoff's theorem really tell us?

Details What does Birkhoff's theorem really tell us? What does Birkhoff's theorem really tell us?

2009-10-27

arxiv.org/abs/0910.5194v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages; 6 figures

Scientific paper

Birkhoff's theorem is a classic result that characterizes locally spherically symmetric solutions of the Einstein equations. In this paper, we illustrate the consequences of its local nature for the cases of vacuum and positive cosmological constant. We construct several examples of initial data for spherically symmetric spacetimes on Cauchy surfaces of different topology than that of the maximal analytic extension of Schwarzschild and Schwarzschild-de Sitter spacetimes. The spacetimes formed from the evolution of these initial data sets also have very different physical properties; in particular they need not contain a static region or be asymptotically flat or asymptotically de Sitter. We also present locally spherically symmetric initial data sets for de Sitter spacetimes that are not covered by the maximal analytic extension of de Sitter spacetime itself. Finally we illustrate the utility of Birkhoff's theorem in identifying the spacetimes associated with two spherically symmetric initial data sets; one proven to exist but not explicitly exhibited and one which has negative ADM mass.

Affiliated with

Also associated with

No associations

Rating

What does Birkhoff's theorem really tell us? 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 What does Birkhoff's theorem really tell us?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and What does Birkhoff's theorem really tell us? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-483700