TWO DIMENSIONAL DILATON GRAVITY COUPLED TO AN ABELIAN GAUGE FIELD

TL;DR

This paper analyzes the most general two-dimensional dilaton gravity coupled to an Abelian gauge field, deriving static solutions, physical properties of black holes, and their quantum characteristics, including entropy and temperature, within a Hamiltonian and WKB framework.

Contribution

It provides a comprehensive Hamiltonian and quantum analysis of 2D dilaton gravity with gauge fields, including explicit solutions and black hole thermodynamics.

Findings

Explicit static solutions with two parameters

Black hole temperature proportional to surface gravity

Quantum phase relates black hole entropy to WKB imaginary part

Abstract

The most general two-dimensional dilaton gravity theory coupled to an Abelian gauge field is considered. It is shown that, up to spacetime diffeomorphisms and $U(1)$ gauge transformations, the field equations admit a two-parameter family of distinct, static solutions. For theories with black hole solutions, coordinate invariant expressions are found for the energy, charge, surface gravity, Hawking temperature and entropy of the black holes. The Hawking temperature is proportional to the surface gravity as expected, and both vanish in the case of extremal black holes in the generic theory. A Hamiltonian analysis of the general theory is performed, and a complete set of (global) Dirac physical observables is obtained. The theory is then quantized using the Dirac method in the WKB approximation. A connection between the black hole entropy and the imaginary part of the WKB phase of the Dirac quantum wave functional is found for arbitrary values of the mass and $U(1)$ charge. The imaginary part of the phase vanishes for extremal black holes and for eternal, non-extremal Reissner-Nordstrom black holes.