Supergravity p-branes revisited: extra parameters, uniqueness, and topological censorship

TL;DR

This paper provides a comprehensive analysis of black p-branes in various topologies, establishing uniqueness theorems, exploring parameter spaces, and demonstrating topological censorship, with extensions to solutions involving a cosmological constant.

Contribution

It offers a complete integration of Einstein-dilaton-antisymmetric form actions for p-branes, proving uniqueness and topological censorship, and deriving new solutions with a cosmological constant.

Findings

Asymptotically flat solutions form a five-parameter subspace.

Regular horizons restrict parameters to relate to mass, charge, and dilaton.

No solutions with toroidal or hyperbolic topology satisfy standard conditions.

Abstract

We perform a complete integration of the Einstein-dilaton-antisymmetric form action describing black p-branes in arbitrary dimensions assuming the transverse space to be homogeneous and possessing spherical, toroidal or hyperbolic topology. The generic solution contains eight parameters satisfying one constraint. Asymptotically flat solutions form a five-parametric subspace, while conditions of regularity of the non-degenerate event horizon further restrict this number to three, which can be related to the mass and the charge densities and the asymptotic value of the dilaton. In the case of a degenerate horizon, this number is reduced by one. Our derivation constitutes a constructive proof of the uniqueness theorem for $p$-branes with the homogeneous transverse space. No asymptotically flat solutions with toroidal or hyperbolic transverse space within the considered class are shown to exist, which result can be viewed as a demonstration of the topological censorship for p-branes. From our considerations it follows, in particular, that some previously discussed p-brane-like solutions with extra parameters do not satisfy the standard conditions of asymptotic flatness and absence of naked singularities. We also explore the same system in presence of a cosmological constant, and derive a complete analytic solution for higher-dimensional charged topological black holes, thus proving their uniqueness.