Exact Physical Black Hole States in Generic 2-D Dilaton Gravity

TL;DR

This paper derives exact quantum states of black holes in generic 2-D dilaton gravity, revealing a continuous spectrum in Lorentzian signature and a quantized entropy in Euclidean signature, applicable to various models including string-inspired theories.

Contribution

It provides an exact solution to the quantum Dirac constraints for black holes in generic 2-D dilaton gravity, connecting geometric phase space variables to physical eigenstates.

Findings

Exact eigenstates of the energy operator are obtained.

The spectrum is continuous in Lorentzian signature.

The Euclidean entropy is quantized as 2πn/G.

Abstract

The quantum mechanics of black holes in generic 2-D dilaton gravity is considered. The Hamiltonian surface terms are derived for boundary conditions corresponding to an eternal black hole with slices on the interior ending on the horizon bifurcation point. The quantum Dirac constraints are solved exactly for these boundary conditions to yield physical eigenstates of the energy operator. The solutions are obtained in terms of geometrical phase space variables that were originally used by Cangemi, Jackiw and Zwiebach in the context of string inspired dilaton gravity. The spectrum is continuous in the Lorentzian sector, but in the Euclidean sector the thermodynamic entropy must be $2\pi n/G$ where $n$ is an integer. The general class of models considered contains as special cases string inspired dilaton gravity, Jackiw-Teitelboim gravity and spherically symmetry gravity.