Abstract
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles. We discuss how this may lead to a gross violation of black hole uniqueness, beyond the existence of black rings, even for solutions with two commuting rotational symmetries. We illustrate this with a simple example in minimal supergravity; a four parameter family of supersymmetric black hole solutions, with spherical horizon topology and a 2-cycle in the exterior. We show there are black holes in this family with identical conserved changes to the BMPV black hole, thereby demonstrating black hole non-uniqueness in this context. We find a decoupling limit of this family of black holes that yields spacetimes asymptotic to the near-horizon geometry of a BMPV black hole which contain a black hole and an exterior 2-cycle.
Highlights
A supersymmetric exampleLarge families of supersymmetric smooth solitons with bubbles have been constructed in the ‘fuzzball’ literature [24]
The known solutions consist of the Myers-Perry black holes and the black rings, which have horizon topologies H ∼= S3 and H ∼= S1 × S2 respectively, see [9] for a review
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles. We discuss how this may lead to a gross violation of black hole uniqueness, beyond the existence of black rings, even for solutions with two commuting rotational symmetries. We illustrate this with a simple example in minimal supergravity; a four parameter family of supersymmetric black hole solutions, with spherical horizon topology and a 2-cycle in the exterior
Summary
Large families of supersymmetric smooth solitons with bubbles have been constructed in the ‘fuzzball’ literature [24]. It is a simple matter to ‘add’ a black hole to such ‘bubbling’ geometries. This has not really been emphasised in the literature, presumably because the focus of the fuzzball program has been on smooth geometries rather than black holes. We will discuss the simplest possibility of an asymptotically flat black hole solution to minimal supergravity with S3 horizon topology possessing one exterior bubble. We will first write down the solution and discuss its salient features
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