Quantum evolution of near-extremal Reissner–Nordström black holes

Abstract

We study the near-horizon AdS 2 ×S 2 geometry of evaporating near-extremal Reissner-Nordström black holes interacting with null matter. The non-local (boundary) terms t ± , 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.

Dilaton gravity in two dimensions

“…The action (7.75) already incorporates all quantum effects, because in this case no higher loop corrections exist, a feature used in refs. [146,145,55] to extend the one-loop calculations to all orders of perturbation theory. The method of exact functional integration described here seems to be a rather general one, although it does not seem possible to formulate general criteria of applicability.…”

Quantum corrections for a Bañados-Teitelboim-Zanelli black hole via the 2D reduced model

“…AdS 2 × S 2 geometry appears as the near horizon geometry of the extermal Reisner-Nordström solution and it is analyzed in [30,31,32]. For the value of constant C = 2r + l 2 we get the components of EMT:…”

“…Different vacuum states were, in the framework of Reisner-Nordström geometry, discussed by Spradelin and Strominger [30]. Fabbri, Navarro and Navarro-Salas considered the one-loop corrections for evaporating AdS 2 black hole [31,32], but again in the connection with Reisner-Nordström geometry. Now, we want to find the one-loop solution of this model.…”

Evaporation of Charged Black Holes Near Extremality

“…If, in addition, we also consider spherically reduced configurations, the theory can be described, in a region very close to the horizon, by a solvable effective model. This model is just the Jackiw-Teitelboim model [2] (for details see [3])where the two-dimensional fields of (1) are related to the four-dimensional metric by the expression ds The above expression contains a cosmological term with λ 2 = l −2 q −3 to ensure that the extremal geometry remains an exact solution of the one-loop theory. The equations of motion derived from I + I P L in conformal gauge ds 2 = −e 2ρ dx + dx − are …”

“…If, in addition, we also consider spherically reduced configurations, the theory can be described, in a region very close to the horizon, by a solvable effective model. This model is just the Jackiw-Teitelboim model [2] (for details see [3])…”