Gravitating Opposites Attract

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 $n+1$ ($n\ge 3$) 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.

13 pages; slightly amended version, some references added, matches version to be published in Classical and Quantum Gravity

References in corpus (9)

• Opposites Attract - A Theorem About The Casimir Force
• The Maximum Tension Principle in General Relativity
• Comment on the sign of the Casimir force
• The double-Reissner-Nordstrom solution and the interaction force between two spherically symmetric charged particles
• On the interaction between two Kerr black holes
• Celestial mechanics of elastic bodies
• On Static n-body Configurations in Relativity
• A Double Myers-Perry Black Hole in Five Dimensions
• How Special Relativity Determines the Signs of the Nonrelativistic, Coulomb and Newtonian, Forces

Cited by in corpus (8)

• Stationary Black Holes: Uniqueness and Beyond
• Stationary two-black-hole configurations: A non-existence proof
• Non-existence of stationary two-black-hole configurations: The degenerate case
• Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria
• Rotating Electroweak Sphaleron-Antisphaleron Systems
• Non-existence of multiple-black-hole solutions close to Kerr-Newman
• Properties of Charged Rotating Electroweak Sphaleron-Antisphaleron Systems
• Self-gravitating elastic bodies