The dualities of 3D dilaton gravity

TL;DR

This paper explores the symmetries and solutions of 3D dilaton gravity theories, revealing dualities between black string solutions and spacetimes with conical singularities, and discussing their implications in string theory and general relativity.

Contribution

It identifies an O(2) symmetry in 3D dilaton gravity equations and derives new static and cosmological solutions, including dualities between different spacetime configurations.

Findings

Discovered an O(2) symmetry in the reduced field equations.

Derived general static and cosmological solutions.

Established duality between black string and conical singularity solutions.

Abstract

We investigate Brans-Dicke dilaton gravity theories in 2+1 dimensions. We show that the reduced field equations for solutions with diagonal metric and depending only on one spacetime coordinate have a continuous O(2) symmetry. Using this symmetry we derive general static and cosmological solutions of the theory. The action of the discrete group O(2,Z) on the space of the solutions is discussed. Three-dimensional string effective theory and three-dimensional general relativity are discussed in detail. In particular, we find that the previously discovered black string solution is dual to a spacetime with a conical singularity.