A new proof of Birkhoff's theorem
| dc.creator | Schmidt, H. -J. | |
| dc.date | 1997-09-26 | |
| dc.date.accessioned | 2026-07-07T06:32:26Z | |
| dc.date.available | 2026-07-07T06:32:26Z | |
| dc.description | Assuming SO(3)-spherical symmetry, the 4-dimensional Einstein equation reduces to an equation conformally related to the field equation for 2-dimensional gravity following from the Lagrangian L = R^(1/3). Solutions for 2-dimensional gravity always possess a local isometry because the traceless part of its Ricci tensor identically vanishes. Combining both facts, we get a new proof of Birkhoff's theorem; contrary to other proofs, no coordinates must be introduced. The SO(m)-spherically symmetric solutions of the (m+1)-dimensional Einstein equation can be found by considering L = R^(1/m) in two dimensions. This yields several generalizations of Birkhoff's theorem in an arbitrary number of dimensions, and to an arbitrary signature of the metric. | |
| dc.description | 17 pages, LaTeX, no figures, Grav. and Cosm. in print | |
| dc.identifier | https://arxiv.org/abs/gr-qc/9709071 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/9709071 | |
| dc.identifier | Grav.Cosmol. 3 (1997) 185-190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98900 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | A new proof of Birkhoff's theorem | |
| dc.type | text |