Gravitating Brane Systems: Some General Theorems

TL;DR

This paper explores the general properties of multidimensional gravity coupled with intersecting p-branes, establishing theorems on cosmological asymptotics, black hole uniqueness, and restrictions on wormholes without solving complex field equations.

Contribution

It provides new general theorems on the asymptotic behavior, black hole uniqueness, and wormhole restrictions in multidimensional p-brane systems, without requiring explicit solutions.

Findings

Asymptotic properties of isotropic cosmologies are characterized.

A no-hair-type theorem for black holes is proved.

Non-existence of Lorentzian wormholes in these models is established.

Abstract

Multidimensional gravity interacting with intersecting electric and magnetic $p$-branes is considered for fields depending on a single variable. Some general features of the system behaviour are revealed without solving the field equations. Thus, essential asymptotic properties of isotropic cosmologies are indicated for different signs of spatial curvature; a no-hair-type theorem and a single-time theorem for black holes are proved (the latter makes sense in models with multiple time coordinates). The validity of the general observations is verified for a class of exact solutions known for the cases when certain vectors, built from the input parameters of the model, are either orthogonal in minisuperspace, or form mutually orthogonal subsystems. From the non-existence of Lorentzian wormholes, a universal restriction is obtained, applicable to orthogonal or block-orthogonal subsystems of any $p$-brane system.