Extreme black hole anabasis

We study the 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 AdS(2)x S-2 boundary and builds the exterior of an asymptotically flat Reissner-Nordstrom black hole with Q=M1-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 AdS(2)xS(2). The connected AdS(2) is a nearly-AdS(2) with its SL(2) broken appropriately for it to maintain connection to the asymptotically flat region of Reissner-Nordstrom. We perform a backreaction calculation with matter in the connected AdS(2)x S-2 and show that it correctly captures the dynamics of the asymptotically flat black hole.

Automated summary

We identified an invariant mu characterizing a backreaction in the study of spherically symmetric perturbations of the Bertotti-Robinson universe. The only allowed backreaction destroys the AdS(2)xS-2 boundary and builds the exterior of an asymptotically flat Reissner-Nordstrom black hole. Addition of linear anabasis perturbations to Bertotti-Robinson defines a connected AdS(2)xS(2) which accurately captures the dynamics of the asymptotically flat black hole.