Rigidity theorems in the braneworld model

TL;DR

This paper establishes rigidity theorems for vacuum branes in static bulk spacetimes, demonstrating constraints on black hole presence and characterizing certain solutions as black strings within braneworld models.

Contribution

It provides new rigidity theorems for vacuum branes, showing limitations on black hole configurations and identifying conditions for black string solutions.

Findings

Vacuum branes with certain symmetries cannot host black holes.

Static bulk spacetimes with specific foliations are identified as black string solutions.

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.