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

Gabor Kunstatter·Jorma Louko
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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.

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Gabor Kunstatter, Jorma Louko. 2007-02-02. Transgressing the horizons: Time operator in two-dimensional dilaton gravity. https://doi.org/10.1103/physrevd.75.024036

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