Abstract
We study the SL(2) transformation properties of spherically symmetric perturbations of the Bertotti-Robinson universe and identify an invariant μ that characterizes the backreaction of these linear solutions. The only backreaction allowed by Birkhoff’s theorem is one that destroys the AdS2 × S2 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 AdS2 ×S2. The connected AdS2 is a nearly-AdS2 with its 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 AdS2 × S2 and show that it correctly captures the dynamics of the asymptotically flat black hole.
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Hadar, S., Lupsasca, A. & Porfyriadis, A.P. Extreme black hole anabasis. J. High Energ. Phys. 2021, 223 (2021). https://doi.org/10.1007/JHEP03(2021)223
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DOI: https://doi.org/10.1007/JHEP03(2021)223