Gravitating Opposites Attract

TL;DR

This paper proves the non-existence of certain symmetric stationary configurations in various theories of gravity, including General Relativity and supergravity, extending previous results to higher dimensions and more complex matter fields.

Contribution

It generalizes prior non-existence theorems to include higher-dimensional spacetimes and additional matter fields like scalars and vectors, covering supergravity and Kaluza-Klein models.

Findings

Proves non-existence of symmetric stationary configurations in GR and supergravity.

Extends results to higher dimensions ($n+1$, $n \u003e= 3$).

Includes configurations with scalar and vector fields in supergravity.

Abstract

Generalizing previous work by two of us, we prove the non-existence of certain stationary configurations in General Relativity having a spatial reflection symmetry across a non-compact surface disjoint from the matter region. Our results cover cases such that of two symmetrically arranged rotating bodies with anti-aligned spins in $n+1$ ($n \geq 3$) dimensions, or two symmetrically arranged static bodies with opposite charges in 3+1 dimensions. They also cover certain symmetric configurations in (3+1)-dimensional gravity coupled to a collection of scalars and abelian vector fields, such as arise in supergravity and Kaluza-Klein models. We also treat the bosonic sector of simple supergravity in 4+1 dimensions.