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      On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions

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          Abstract

          We study the class of vacuum (Ricci flat) six-dimensional spacetimes admitting a non-degenerate multiple Weyl aligned null direction \(\ell\), thus being of Weyl type II or more special. Subject to an additional assumption on the asymptotic fall-off of the Weyl tensor, we prove that these spacetimes can be completely classified in terms of the two eigenvalues of the (asymptotic) twist matrix of \(\ell\) and of a discrete parameter \(U^0=\pm 1/2, 0\). All solutions turn out to be Kerr-Schild spacetimes of type D and they reduce to a family of "generalized" Myers-Perry metrics (which include limits and analytic continuations of the original Myers-Perry metric, such as certain NUT spacetimes). A special subcase corresponds to twisting solutions with zero shear.

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          Black holes in higher dimensional space-times

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            Schwarzschild field inn dimensions and the dimensionality of space problem

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              Topological Black Holes in Anti-de Sitter Space

              We consider a class of black hole solutions to Einstein's equations in d dimensions with a negative cosmological constant. These solutions have the property that the horizon is a (d-2)-dimensional Einstein manifold of positive, zero, or negative curvature. The mass, temperature, and entropy are calculated. Using the correspondence with conformal field theory, the phase structure of the solutions is examined, and used to determine the correct mass dependence of the Bekenstein-Hawking entropy.
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                Author and article information

                Journal
                2016-10-25
                Article
                1610.07750
                5fbb6dea-4e96-4819-92aa-bf122900d383

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                29 pages
                gr-qc hep-th

                General relativity & Quantum cosmology,High energy & Particle physics
                General relativity & Quantum cosmology, High energy & Particle physics

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