On T-duality in dilatonic gravity

TL;DR

This paper introduces a T-duality framework for dilatonic gravity under axial symmetry, mapping it to a string-like action and revealing an $SO(2,1)$ duality group that recovers known symmetries.

Contribution

It presents a novel method to implement string theory T-duality in dilatonic gravity using a new mapping under axial symmetry, with a specific focus on an $SO(2,1)$ duality group.

Findings

Established a map from dilatonic gravity to a string-like action.

Defined an $SO(2,1)$ duality group for the theory.

Recovered a known symmetry of dilatonic gravity.

Abstract

Under the assumption of axial symmetry we introduce a map from dilatonic gravity to a string-like action. This map allows one to introduce, in a rather simple way, the equivalent of string theory T-duality in dilatonic gravity. Here we choose the duality group to be an $SO(2,1)$ group and, for a particular rotation, we recover a symmetry of dilatonic gravity discussed previously in the literature.