A Unitary S-matrix for 2D 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.

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.

1995

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. 1 Work supported by MNTRS and Royal Society

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.

2024

We numerically calculate the spacetime describing the formation and evaporation of a regular black hole in 2D dilaton gravity. The apparent horizons evaporate smoothly in finite time to form a compact trapped region. We nevertheless see rich dynamics: an antitrapped region forms alongside the black hole and additional compact trapped and antitrapped regions are formed by backreaction effects as the mass radiates away. The spacetime is asymptotically flat at future null infinity and is free of singularities and Cauchy horizons. These results suggest that the evaporation of regular 2D black holes is unitary.

Physical Review Letters, 2008

We analyze Hawking evaporation of the Callan-Giddings-Harvey-Strominger (CGHS) black holes from a quantum geometry perspective and show that information is not lost, primarily because the quantum space-time is sufficiently larger than the classical. Using suitable approximations to extract physics from quantum space-times we establish that: i)future null infinity of the quantum space-time is sufficiently long for the the past vacuum to evolve to a pure state in the future; ii) this state has a finite norm in the future Fock space; and iii) all the information comes out at future infinity; there are no remnants.

Proceedings of the 6th Canadian Conference on General Relativity and Relativistic Astrophysics, 1997

The two-dimensional CGHS model provides an interesting toymodel for the study of black hole evaporation. For this model, a quantum effective action, which incorporates Hawking radiation and backreaction, can be explicitly constructed. In this paper, we study a generalization of this effective action. In our extended model, it is possible to remove certain curvature singularities arising for the original theory. We also find that the flux of Hawking radiation is identical to that encountered in other two-dimensional models.

Physical Review Letters - PHYS REV LETT, 2008

We analyze Hawking evaporation of the Callen-Giddings-Harvey-Strominger (CGHS) black holes from a quantum geometry perspective and show that information is not lost, primarily because the quantum space-time is sufficiently larger than the classical. Using suitable approximations to extract physics from quantum space-times we establish that: i)future null infinity of the quantum space-time is sufficiently long for the the past vacuum to evolve to a pure state in the future; ii) this state has a finite norm in the future Fock space; and iii) all the information comes out at future infinity; there are no remnants.

2005

The formation and evaporation of a black hole can be viewed as a scattering process in Quantum Gravity. Semiclassical arguments indicate that the process should be non-unitary, and that all the information of the original quantum state forming the black hole should be lost after the black hole has completely evaporated, except for its mass, charge and angular momentum. This would imply a violation of basic principles of quantum mechanics. We review some proposed resolutions to the problem, including developments in string theory and a recent proposal by Hawking. We also suggest a novel approach which makes use of some ingredients of earlier proposals. [Based on Talks given at ERE2004 "Beyond General Relativity", Miraflores de la Sierra, Madrid (Sept 2004), and at CERN (Oct 2004)].

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.