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Rigidity theorems in the braneworld model

Hideo Kodama
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Abstract

In the present paper, we give some theorems representing ridigity of a vacuum brane in static bulk spacetimes. As an application, we show that a static bulk spacetime with dimension D>3 and spatial symmetry IO(D-2), O(D-1) or O_+(D-2,1) does not allow a vacuum brane with a black hole on it. We also show that if a static bulk spacetime with dimension D>4 satsifying the vacuum Einstein equations can be foliated by a continuous family of vacuum branes with asymptotically constant curvature, it is a black string solution.

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Hideo Kodama. 2002-05-01. Rigidity theorems in the braneworld model. https://doi.org/10.1143/ptps.148.277

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