Extreme Black Hole Anabasis

Abstract

We study the $\mathsf{SL}(2)$ transformation properties of spherically symmetric perturbations of the Bertotti-Robinson universe and identify an invariant $\mu$ that characterizes the backreaction of these linear solutions. The only backreaction allowed by Birkhoff's theorem is one that destroys the $Ad{S}_2\times S^2$ boundary and builds the exterior of an asymptotically flat Reissner-Nordström black hole with $Q=M\sqrt{1-\mu /4}$. We call such backreaction with boundary condition change an anabasis. We show that the addition of linear anabasis perturbations to Bertotti-Robinson may be thought of as a boundary condition that defines a connected $Ad{S}_2\times S^2$. The connected $Ad{S}_2$ is a nearly-$Ad{S}_2$ with its $\mathsf{SL}(2)$ broken appropriately for it to maintain connection to the asymptotically flat region of Reissner-Nordström. We perform a backreaction calculation with matter in the connected $Ad{S}_2\times S^2$ and show that it correctly captures the dynamics of the asymptotically flat black hole.

20 pages, 4 figures; v2: typo corrected, refs added; v3: minor edits, more refs added, matches published version

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Cited by in corpus (1)

• Horizon Acoustics of the GHS Black Hole and the Spectrum of ${\mathrm{AdS}}_2$