Laplacian in the hyperbolic space Hn and linearization stability of the Einstein equation for Robertson-Walker models
We prove that some operators related to the rough Laplacian in the hyperbolic space give isomorphisms between Sobolev spaces of 1-forms. By using these results we prove that the Einstein equation of t...
We prove that some operators related to the rough Laplacian in the hyperbolic space give isomorphisms between Sobolev spaces of 1-forms. By using these results we prove that the Einstein equation of t...
The Kepler problem with anisotropic perturbations
We study a two-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree –, 2. For >2, the sets of initial conditions leadi...
We study a two-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree –, 2. For >2, the sets of initial conditions leadi...
Birkhoff's theorem in Lovelock gravity
J. Math. Phys. 46, 072502 (2005); doi:10.1063/1.1960798
Published 15 July 2005
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We show that the solutions of the Lovelock equations with spherical, planar, or hyperbolic symmetry are locally isometric to the corresponding static Lovelock black hole. As a consequence, these solutions are locally static: they admit an additional Killing vector that can either be space-like or time-like, depending on the position. This result also holds in the presence of an abelian gauge field, in which case the solutions are locally isometric to a charged static black hole.
©2005 American Institute of Physics
| History: | Received 16 May 2005; accepted 27 May 2005; published 15 July 2005 |
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http://link.aip.org/link/?JMAPAQ/46/072502/1 |
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