Abstract
The multicenter solutions of 4d ${\cal N}=2$ supergravity contain a subset of scaling solutions with vanishing total angular momentum. In a near limit those solutions are asymptotically locally AdS$_2\times$ S$^2$, but we show that a higher moment of angular momentum contributes a subtle twist, rotating the S$^2$ with time. This provides some potential hair distinguishing the asymptotics of these scaling solutions from the near horizon geometry of an extremal BPS black hole.
Highlights
The multicenter solutions of four-dimensional N 1⁄4 2 supergravity contain a subset of scaling solutions with vanishing total angular momentum
In a near limit those solutions are asymptotically locally AdS2 × S2, but we show that a higher moment of angular momentum contributes a subtle twist, rotating the S2 with time
The multicentered black hole solutions of fourdimensional N 1⁄4 2 supergravity [1,2,3] provide an interesting setting to investigate the Bogomol'nyi-PrasadSommerfield (BPS) spectrum of string theory compactified on a Calabi-Yau manifold and the associated physics problem of black hole entropy and microstates [4,5,6,7,8]
Summary
The multicentered black hole solutions of fourdimensional N 1⁄4 2 supergravity [1,2,3] provide an interesting setting to investigate the Bogomol'nyi-PrasadSommerfield (BPS) spectrum of string theory compactified on a Calabi-Yau manifold and the associated physics problem of black hole entropy and microstates [4,5,6,7,8]. It is in this setting that recently a subset of multicenter solutions, often called “scaling solutions” [5,13,14,15], has been revisited and its asymptotic AdS2 nature explored [16]; see [17,18] In this short article we point out that somewhat surprisingly the asymptotic geometry typically has a fibred structure, with an S2 rotating over AdS2. Since it has been argued that precisely the scaling solutions correspond to the exponential majority of black hole microstates [19,20,21], a precise holographic interpretation of the twist would be highly interesting We leave this last problem for future work. For a generic multicenter solution these fields and the metric take the following form: ds
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