Vacuum branes in D-dimensional static spacetimes with spatial symmetry IO(D-2), O(D-1) or O+(D-2,1)

Abstract

In this paper, we give a complete classification of vacuum branes, i.e., everywhere umbilical time-like hypersurfaces whose extrinsic curvature is a constant multiple of the induced metric, K_mn=k g_mn, in D-dimensional static spacetimes with spatial symmetry G(D-2,K), where G(n,K) is the isometry group of an n-dimensional space with constant sectional curvature K. D>=4 is assumed. It is shown that all possible configurations of a brane are invariant under an isometry subgroup G(D-3,K') for some K'>= K. In particular, configurations of a brane with non-zero k are always G(D-2,K) invariant, except for those in five special one-parameter families of spacetimes. Further, such G(D-2,K)-invariant configurations are allowed only in spacetimes whose Ricci tensors are isotropic in the two planes orthogonal to each G(D-2,K)-orbit, or for special values of k, which do not exist in generic cases. On the basis of these results, we prove the non-existence of a vacuum brane with black hole geometry in static bulk spacetimes with spatial symmetry G(D-2,K). We also discuss mathematical implications of these results.

42 pages in LaTeX with the PTP style. No figure. Minor errors are corrected, and notations are partially changed

Cited by in corpus (8)

• Small localized black holes in a braneworld: Formulation and numerical method
• Six-dimensional localized black holes: numerical solutions
• Decay of Massive Dirac Hair on a Brane-World Black Hole
• Asymptotically AdS brane black holes
• Decay of massive hair on brane black hole
• Thermodynamics of four-dimensional black objects in the warped compactification
• Naked shell singularities on the brane
• Accelerating a Black Hole in Higher Dimensions