Static Quantization of Two-dimensional Dilaton Gravity and Black Holes

TL;DR

This paper explores the quantization of two-dimensional dilaton gravity, revealing a gauge-invariant quantum mechanics framework and analyzing the properties of physical operators and states, with implications for higher-dimensional spherical gravity.

Contribution

It introduces a static quantization approach for 2D dilaton gravity, providing insights into the self-adjointness of the ADM mass operator in symmetric higher-dimensional gravity.

Findings

The quantum theory is gauge invariant and reduces to quantum mechanics.

The ADM mass squared operator is self-adjoint, not the mass itself.

Provides a framework for analyzing physical states in 2D and higher-dimensional gravity.

Abstract

Two-dimensional matterless dilaton gravity is a topological theory and can be classically reduced to a (0+1)-dimensional theory with a finite number of degrees of freedom. If quantization is performed, a simple gauge invariant quantum mechanics is obtained. The properties of the gauge invariant operators and of the Hilbert space of physical states can be determined. In particular, for N-dimensional pure gravity with (N-2)-dimensional spherical symmetry, the square of the ADM mass operator is self-adjoint, not the mass itself.