Rigidity theorems in the braneworld model
Abstract
Description
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.
7 pages in LaTeX with the PTP style. No figure. To be published in the proceedings of the workshop "Braneworld -- Dynamics of spacetime with boundary --"
7 pages in LaTeX with the PTP style. No figure. To be published in the proceedings of the workshop "Braneworld -- Dynamics of spacetime with boundary --"