Abstract
We explore the bubble spacetimes which can be obtained from double analytic continuations of static and rotating black holes in anti-de Sitter space. In particular, we find that rotating black holes with elliptic horizon lead to bubble spacetimes only in dimension greater than five. For dimension greater than seven, the topology of the bubble can be non-spherical. However, a bubble spacetime is shown to arise from a rotating de Sitter black hole in four dimensions. In all cases, the evolution of the bubble is of de Sitter type. Double analytic continuations of hyperbolic black holes and branes are also discussed.
Highlights
The formulation of string theory in time-dependent backgrounds presents a challenging problem, progress can be achieved by considering some simple time-dependent solutions
Our aim here is to investigate the bubble spacetimes which can be obtained from the analytic continuation of black holes in de Sitter and anti-de Sitter space
We find that the static and rotating black holes with elliptic horizon lead to bubbles which have only a de Sitter phase of evolution
Summary
The formulation of string theory in time-dependent backgrounds presents a challenging problem, progress can be achieved by considering some simple time-dependent solutions. The technique of double analytic continuation was originally developed for the study of the stability of the Kaluza–Klein vacuum [2], see [3,4] This technique has been used in the formulation of a positive energy theorem for anti-de Sitter space [5], and discussed within the context of brane world scenarios [6,7], and M-theory [8,9]. Our aim here is to investigate the bubble spacetimes which can be obtained from the analytic continuation of black holes in de Sitter and anti-de Sitter space In the latter case, there is wide class of topological black hole spacetimes available, due to the possibility of non-trivial horizon topology [10,11,12,13,14,15,16,17]. We show that a bubble spacetime does arise from the rotating de Sitter black hole in four dimensions
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