On Birkhoff's theorem in ghost-free bimetric theory

We consider the Hassan-Rosen bimetric field equations in vacuum when the two metrics share a single common null direction in a spherically symmetric configuration. By solving these equations, we obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. B...

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Published inarXiv.org
Main Authors Kocic, Mikica, Högås, Marcus, Torsello, Francesco, Mortsell, Edvard
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.08.2017
Subjects
Fields (mathematics)
Mathematical analysis
Physics - General Relativity and Quantum Cosmology
Physics - High Energy Physics - Theory
Theorems
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Summary:We consider the Hassan-Rosen bimetric field equations in vacuum when the two metrics share a single common null direction in a spherically symmetric configuration. By solving these equations, we obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. Besides not being asymptotically flat, the found solutions are nonstationary admitting only three global spacelike Killing vector fields which are the generators of spatial rotations. Hence, these are spherically symmetric bimetric vacuum solutions with the minimal number of isometries. The absence of staticity formally disproves an analogue statement to Birkhoff's theorem in the ghost-free bimetric theory which would state that a spherically symmetric solution is necessarily static in empty space.
ISSN:2331-8422
DOI:10.48550/arxiv.1708.07833