Conservation Laws and 2D Black Holes in Dilaton Gravity

TL;DR

This paper explores conservation laws in a broad class of 2D dilaton gravity models, deriving conditions for symmetries and presenting new black hole solutions with unique thermodynamic features.

Contribution

It introduces a general framework for conservation laws in 2D dilaton gravity and presents novel black hole solutions with distinct thermodynamic properties.

Findings

Existence of a conserved stress-energy vector field independent of equations of motion.

Derived conditions for the presence of Killing vectors in these models.

Found new 2D black hole solutions resembling string-theoretic black holes with different thermodynamics.

Abstract

A very general class of Lagrangians which couple scalar fields to gravitation and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved, regardless of whether or not the equations of motion are satisfied or if any Killing vectors exist. Conditions necessary for the existence of Killing vectors are derived. A new set of 2D black hole solutions is obtained for one particular member within this class of Lagrangians. One such solution bears an interesting resemblance to the 2D string-theoretic black hole, yet contains markedly different thermodynamic properties.