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

TL;DR

This paper develops a quantum framework for two-dimensional black holes, introducing a time operator that accounts for quantum corrections to horizon properties, advancing understanding of quantum gravity effects near horizons.

Contribution

It presents a Dirac quantization of black holes in 2D dilaton gravity with a novel time operator that incorporates quantum corrections across horizons.

Findings

Quantum correction distinguishes future and past horizons.

Time operator regularity requires quantum correction.

Quantum correction affects surface gravity of black holes.

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.