Two-Dimensional Dilaton Black Holes (original) (raw)

Unitary theory of evaporating two-dimensional black holes

Classical and Quantum Gravity, 1996

We study a manifestly unitary formulation of 2d dilaton quantum gravity based on the reduced phase space quantization. The spacetime metric operator can be expanded in a formal power series of the matter energymomentum tensor operator. This expansion can be used for calculating the quantum corrections to the classical black hole metric by evaluating the expectation value of the metric operator in an appropriate class of the physical states. When the normal ordering in the metric operator is chosen to be with respect to Kruskal vacuum, the lowest order semiclassical metric is exactly the one-loop effective action metric discovered by Bose, Parker and Peleg. The corresponding semiclassical geometry describes an evaporating black hole which ends up as a remnant. The calculation of higher order corrections and implications for the black hole fate are discussed.

Unitary Theory of Evaporating 2D Black Holes

July 1995 Imperial/TP/94-95/50 Unitary Theory of Evaporating 2D Black Holes

1995

Static and Nonstatic Quantum Effects in Two-Dimensional Dilaton Gravity

Modern Physics Letters A, 2000

We study back-reaction effects in two-dimensional dilaton gravity. The back-reaction comes from an R2 term which is a part of the one-loop effective action arising from massive scalar field quantization in a certain approximation. The peculiarity of this term is that it does not contribute to the Hawking radiation of the classical black hole solution of the field equations. In the static case we examine the horizon and the physical singularity of the new black hole solutions. Studying the possibility of time dependence we see the generation of a new singularity. The particular solution found still has the structure of a black hole, indicating that nonthermal effects cannot lead, at least in this approximation, to black hole evaporation.

Black Holes and Nonperturbative Canonical 2D Dilaton Gravity

We investigate nonperturbative canonical quantization of two dimensional dilaton gravity theories with an emphasis on the CGHS model. We use an approach where a canonical transformation is constructed such that the constraints take a quadratic form. The required canonical transformation is obtained by using a method based on the Bäcklund transformation from the Liouville theory. We quantize dilaton gravity in terms of the new variables, where it takes a form of a bosonic string theory with background charges. Unitarity is then established by going into a light-cone gauge. As a direct consequence, black holes in this theory do not violate unitarity, and there is no information loss. We argue that the information escapes during the evaporation process. We also discuss the implications of this quantization scheme for the quantum fate of real black holes. The main conclusion is that black holes do not have to violate quantum mechanics.

A quantum S-matrix for two-dimensional black hole formation and evaporation

Nuclear Physics B, 1993

We study the black hole information paradox in the context of a two-dimensional toy model given by dilaton gravity coupled to N massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize the theory and derive the quantum S-matrix for the case that N=24. This S-matrix is unitary by construction, and we further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity S-matrix and that of the c = 1 matrix model. * Note that in the spherically symmetric reduction of the Einstein theory, the line e −2φ = 0 coincides with the origin at r = 0 and indeed defines a reflecting boundary. † In [9] this vacuum energy was taken to be proportional to N-24. It will be shown later that (2.6) is the correct value, at least for N = 24.

4-DIMENSIONAL and 2-DIMENSIONAL Evaporating Dilatonic Black Holes

Modern Physics Letters A, 1994

The picture of S-wave scattering from a 4-D extremal dilatonic black hole is examined. Classically, a small matter shock wave will form a non-extremal black hole. In the “throat region” the r-t geometry is exactly that of a collapsing 2-D black hole. The 4-D Hawking radiation (in this classical background) gives the 2-D Hawking radiation exactly in the throat region. The 4-D geometry outside the throat region is almost the extremal one, and the deviations can be calculated using a linear approximation. Inclusion of the back-reaction changes this picture: the linear approximation is valid only at the beginning of the evaporating process. We give (explicitly) that linear 4-D solution. The linear approximation breaks down even before an apparent horizon is formed, which suggests that the 4-D semiclassical solution may be quite different from the 2-D one.

Effective action and Hawking radiation for dilaton coupled scalars in two dimensions

Physical Review D, 1999

The effective one-loop action for general dilaton theories with arbitrary dilaton-dependent measure and nonminimal coupling to scalar matter is computed. As an application we determine the Hawking flux to infinity from black holes in d-dimensions. We resolve the recently resurrected problem of an apparent negative flux for nonminimally coupled scalars: For any D ≥ 4 Black Hole the complete flux turns out to be precisely the one of minimal coupling. This result is obtained from a Christensen-Fulling type argument involving the (non-)conservation of energy-momentum. It is verified also directly from the effective action.

Liouville models of black hole evaporation

Nuclear Physics B, 1993

A renormalizable two-dimensional quantum field theory, containing a metric, a dilaton and N massless scalar matter fields, has been proposed as a model for black hole evaporation. Essential ingredients are a dilaton-dependent cosmological constant and a Polyakov action reflecting the conformal anomaly. Previous work on this model has been done in the large-N (weak coupling) approximation and clear evidence for Hawking radiation and its back-reaction on the metric has been seen. There are, however, quantum consistency questions since the original model was only designed to be a c = 26 conformal field theory in the weak coupling limit. In this paper we construct new theories, differing from the old only in the dilaton dependence of the cosmological constant, and reducing to it in the weak coupling limit. They are exact c = 26 conformal field theories and presumably consistent frameworks for discussing this problem. We also study the new theories with a change in the Polyakov action proposed by Strominger with a view to eliminating unphysical ghost Hawking radiation. The classical equations of motion of the new theories are explicitly soluble, thus permitting an exact analysis of both static solutions and dynamic scenarios. While the static solutions are, by and large, physically reasonable, the dynamical solutions include puzzling examples where wrong-sign Hawking radiation is stimulated by allowing matter to fall into a static solution. We indicate how the latter problem may be resolved in the full quantum theory.

Two-Dimensional Dilaton Black Holes (original) (raw)

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