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Title: Transgressing the horizons: Time operator in two-dimensional dilaton gravity

Abstract

We present a Dirac quantization of generic single-horizon black holes in two-dimensional dilaton gravity. The classical theory is first partially reduced by a spatial gauge choice under which the spatial surfaces extend from a black or white hole singularity to a spacelike infinity. The theory is then quantized in a metric representation, solving the quantum Hamiltonian constraint in terms of (generalized) eigenstates of the ADM mass operator and specifying the physical inner product by self-adjointness of a time operator that is affinely conjugate to the ADM mass. Regularity of the time operator across the horizon requires the operator to contain a quantum correction that distinguishes the future and past horizons and gives rise to a quantum correction in the hole's surface gravity. We expect a similar quantum correction to be present in systems whose dynamics admits black hole formation by gravitational collapse.

Authors:
 [1];  [2]
  1. Department of Physics and Winnipeg Institute of Theoretical Physics, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9 (Canada)
  2. School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
Publication Date:
OSTI Identifier:
21010906
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.024036; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; CORRECTIONS; COSMOLOGY; EIGENSTATES; GRAVITATION; GRAVITATIONAL COLLAPSE; HAMILTONIANS; MASS; QUANTIZATION; QUANTUM FIELD THEORY; QUANTUM OPERATORS; SINGULARITY; TWO-DIMENSIONAL CALCULATIONS; WHITE HOLES

Citation Formats

Kunstatter, Gabor, and Louko, Jorma. Transgressing the horizons: Time operator in two-dimensional dilaton gravity. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.024036.
Kunstatter, Gabor, & Louko, Jorma. Transgressing the horizons: Time operator in two-dimensional dilaton gravity. United States. doi:10.1103/PHYSREVD.75.024036.
Kunstatter, Gabor, and Louko, Jorma. Mon . "Transgressing the horizons: Time operator in two-dimensional dilaton gravity". United States. doi:10.1103/PHYSREVD.75.024036.
@article{osti_21010906,
title = {Transgressing the horizons: Time operator in two-dimensional dilaton gravity},
author = {Kunstatter, Gabor and Louko, Jorma},
abstractNote = {We present a Dirac quantization of generic single-horizon black holes in two-dimensional dilaton gravity. The classical theory is first partially reduced by a spatial gauge choice under which the spatial surfaces extend from a black or white hole singularity to a spacelike infinity. The theory is then quantized in a metric representation, solving the quantum Hamiltonian constraint in terms of (generalized) eigenstates of the ADM mass operator and specifying the physical inner product by self-adjointness of a time operator that is affinely conjugate to the ADM mass. Regularity of the time operator across the horizon requires the operator to contain a quantum correction that distinguishes the future and past horizons and gives rise to a quantum correction in the hole's surface gravity. We expect a similar quantum correction to be present in systems whose dynamics admits black hole formation by gravitational collapse.},
doi = {10.1103/PHYSREVD.75.024036},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}