Quantum evolution of near-extremal Reissner-Nordstrom black holes
A. Fabbri, D. J. Navarro, J. Navarro-Salas
TL;DR
The paper studies quantum evolution in the near-horizon region of evaporating near-extremal RN black holes by mapping to a two-dimensional JT-like theory with boundary terms from the Polyakov-Liouville action. It shows that treating the non-local boundary functions $t_{±}$ as dynamical leads to a consistent backreaction analysis: at leading order one finds a finite evaporation time with a smooth extremal end, while a full dynamical treatment yields an evaporation process that extends to infinite proper time, aligning with the third law of thermodynamics. The results highlight the potential role of boundary data in storing and transmitting information during evaporation, though a complete understanding of outgoing radiation to infinity requires further work. Overall, the work provides an analytic, thermodynamically consistent framework for quantum effects near extremality in RN black holes and clarifies when extremality acts as a stable endpoint.
Abstract
We study the near-horizon AdS_2\timesS^2 geometry of evaporating near-extremal Reissner-Nordstrom black holes interacting with null matter. The non-local (boundary) terms t_{\pm}, coming from the effective theory corrected with the quantum Polyakov-Liouville action, are treated as dynamical variables. We describe analytically the evaporation process which turns out to be compatible with the third law of thermodynamics, i.e., an infinite amount of time is required for the black hole to decay to extremality. Finally we comment briefly on the implications of our results for the information loss problem.