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.

32 pages, 1 eps figure. v2: references and comments added

References in corpus (51)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Hawking Radiation as Tunneling
• Quantum Geometry and Black Hole Entropy
• Particle production and complex path analysis
• The Two-Nucleon Potential from Chiral Lagrangians
• Dilaton Gravity in Two Dimensions
• Hawking Radiation as Tunneling for Extremal and Rotating Black Holes
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Tunnelling, Temperature and Taub-NUT Black Holes
• Geometrodynamics of Schwarzschild Black Holes
• Hawking temperature in the tunneling picture
• Hawking radiation in different coordinate settings: Complex paths approach
• Hawking Radiation as Tunneling through the Quantum Horizon
• Conformal description of horizon's states
• Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
• On Hawking Radiation as Tunneling with Back-Reaction
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Observables for Two-Dimensional Black Holes
• Renormalization of the Inverse Square Potential
• Area spectrum of the Schwarzschild black hole
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• On Hawking Radiation as Tunneling with Logarithmic Corrections
• Spherically Symmetric Gravity as a Completely Integrable System
• Hamiltonian thermodynamics of the Reissner-Nordström-anti-de Sitter black hole
• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• Large quantum gravity effects: Unexpected limitations of the classical theory
• On Singularity Resolution in Quantum Gravity
• Quantum resolution of black hole singularities
• On the consistency of the constraint algebra in spin network quantum gravity
• An algebraic extension of Dirac quantization: Examples
• Loop constraints: A habitat and their algebra
• Hawking Radiation as Tunneling: the D-dimensional rotating case
• Hamiltonian thermodynamics of the Schwarzschild black hole
• Exact Physical Black Hole States in Generic 2-D Dilaton Gravity
• Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. I. General Theory
• Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
• Hamiltonian thermodynamics of a Lovelock black hole
• Hamiltonian Thermodynamics of Black Holes in Generic 2-D Dilaton Gravity
• Flat slice Hamiltonian formalism for dynamical black holes
• Quantum Theory of Black Holes
• Quantum black holes from null expansion operators
• Hamiltonian Thermodynamics of Charged Black Holes
• Large quantum gravity effects: backreaction on matter
• Quantum Hamiltonian for gravitational collapse
• Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes
• Quantum gravity effects in the CGHS model of collapse to a black hole
• Two-dimensional electron gas in a uniform magnetic field in the presence of a delta-impurity
• Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black holes
• Kruskal coordinates as canonical variables for Schwarzschild black holes
• Quantum-Corrected Entropy for 1+1-Dimensional Gravity Revisited
• Quantum Structure of Space Near a Black Hole Horizon

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• Quantum Gravitational Collapse in the Lemaitre-Tolman-Bondi Model with a Positive Cosmological Constant
• Higher Dimensional Choptuik Scaling in Painleve Gullstrand Coordinates
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