J. Cruz

Solvable models for radiating black holes and area-preserving diffeomorphisms☆

Abstract Solvable theories of 2D dilaton gravity can be obtained from a Liouville theory by suitable field redefinitions. In this paper we propose a new framework to generate 2D dilaton gravity models which can also be exactly solved in the semiclassical approximation. Our approach is based on the recently introduced scheme to quantize massless scalar fields coupled to 2D gravity maintaining invariance under area-preserving diffeomorphisms and Weyl transformations. Starting from the CGHS model with the new effective action we reestablish the full diffeomorphism invariance by means of an adequate family of field redefinitions. The original theory is therefore mapped into a large family of solvable models. We focus our analysis on the one-parameter class of models interpolating between the Russo-Susskind-Thorlacius model and the Bose-Parker-Peleg model. Finally we shall briefly indicate how we can extend our approach to spherically symmetric Einstein gravity coupled to 2D conformal matter.

Black hole evaporation by thermal bath removal

Abstract We study the evaporation process of 2D black holes in thermal equilibrium when the incoming radiation is turned off. Our analysis is based on two different classes of 2D dilaton gravity models which are exactly solvable in the semiclassical approximation including back-reaction. We consider a one parameter family of models interpolating between the Russo-Susskind-Thorlacius and Bose-Parker-Peleg models. We find that the end-state geometry is the same as the one coming from an evaporating black hole formed by gravitational collapse. We also study the quantum evolution of black holes arising in a model with classical action S = 1 2π ∫ d 2 x −g (Rφ + 4λ 2 e βφ ) . The black hole temperature is proportional to the mass and the exact semiclassical solution indicates that these black holes never disappear completely.

Can conformal transformations change the fate of 2D black holes

Abstract By using a classical Liouville-type model of two dimensional dilaton gravity we show that the one-loop theory implies that the fate of a black hole depends on the conformal frame. There is one frame for which the evaporation process never stops and another one leading to a complete disappearance of the black hole. This can be seen as a consequence of the fact that thermodynamic variables are not conformally invariant. In the second case the evaporation always produces the same static and regular end-point geometry, irrespective of the initial state.

Free field realization of cylindrically symmetric Einstein gravity

Abstract Cylindrically reduced Einstein gravity can be regarded as an SL(2,R)/SO(2) sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation we show that the theory can be mapped by a canonical transformation into a set of free fields with a Minkowskian target space. We briefly discuss the quantization in terms of these free-field variables, which is considerably simpler than in the other approaches.

Conformal and non-conformal symmetries in 2D dilaton gravity☆

Abstract We introduce new extra symmetry transformations for generic 2D dilaton-gravity models. These symmetries are non-conformal but special linear combinations of them turn out to be the extra (conformal) symmetries of the CGHS model and the model with an exponential. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an auxiliary invariant metric, we construct one-loop models which maintain the extra symmetry of the classical action.

Integrable models, degenerate horizons and AdS2 black holes

Abstract The near extremal Reissner-Nordstrom black holes in arbitrary dimensions can be modeled by the Jackiw-Teitelboim (JT) theory. The asymptotic Virasoro symmetry of the corresponding JT model exactly reproduces, via Cardys formula, the deviation of the Bekenstein-Hawking entropy of the Reissner-Nordstrom black holes from extremality. We also comment how can we extend this approach to investigate the evaporation process.

Free fields for chiral 2D dilaton gravity

We give an explicit canonical transformation which transforms a generic chiral 2D dilaton gravity model into a free field theory.

A quantum model of Schwarzschild black hole evaporation

Abstract We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show that it cannot be a flat metric.

Symmetries and solvable models for evaporating 2D black holes

Abstract We study the evaporation process of a 2D black hole in thermal equilibrium when the ingoing radiation is suddenly switched off. We also introduce global symmetries of generic 2D dilaton gravity models which generalize the extra symmetry of the CGHS model.