GRAVITATING OPPOSITES ATTRACT

Abstract. Generalizing previous work by two of us, we prove the nonexistence 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 ≥ 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.

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