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The Schwarzschild-de Sitter solution in five-dimensional general relativity briefly revisited

J. B. Fonseca-Neto·C. Romero
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Abstract

We briefly revisit the Schwarzschild-de Sitter solution in the context of five-dimensional general relativity. We obtain a class of five-dimensional solutions of Einstein vacuum field equations into which the four-dimensional Schwarzschild-de Sitter space can be locally and isometrically embedded. We show that this class of solutions is well-behaved in the limit of lambda approaching zero. Applying the same procedure to the de Sitter cosmological model in five dimensions we obtain a class of embedding spaces which are similarly well-behaved in this limit. These examples demonstrate that the presence of a non-zero cosmological constant does not in general impose a rigid relation between the (3+1) and (4+1)-dimensional spacetimes, with degenerate limiting behaviour.

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J. B. Fonseca-Neto, C. Romero. 2007-03-20. The Schwarzschild-de Sitter solution in five-dimensional general relativity briefly revisited. https://doi.org/10.1088/0264-9381%2F24%2F13%2Fn01

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