Non-existence of toroidal cohomogeneity-1 near horizon geometries

Details Non-existence of toroidal cohomogeneity-1 near horizon geometries Non-existence of toroidal cohomogeneity-1 near horizon geometries

2010-08-03

arxiv.org/abs/1008.0520v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages

Scientific paper

We prove that $D\geq 5$ dimensional stationary, non-static near horizon
geometries with (D-3) rotational symmetries subject to the vacuum Einstein
equations including a cosmological constant cannot have toroidal horizon
topology. In D=4 dimensions the same result is obtained under the assumption of
a non-negative cosmological constant.

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