Global conformal symmetry in scalar-tensor theories

TL;DR

This paper investigates a subclass of Horndeski gravity with global conformal and shift symmetries, identifying conserved currents that facilitate integrability and exact solutions for black holes, including charged cases.

Contribution

It derives the general conserved current for global conformal symmetry in Horndeski theories and explores its implications for integrability and black hole solutions.

Findings

Identified the conserved current associated with conformal symmetry in Horndeski theories.

Demonstrated how symmetries enable integrability of black hole solutions.

Extended solutions to include charge via conformal invariance of Maxwell action.

Abstract

We study a subclass of Horndeski gravity which has both global conformal and shift symmetries. Global symmetries are characterised by the presence of a conserved current which has been shown to be of particular importance for the integrability features of the theory at hand yielding numerous compact object solutions. We find the general conserved current associated to global conformal symmetry of Horndeski theories. We discuss some of its properties, how it can be conveniently broken by physically relevant terms and, show how it is related to that of shift symmetry when shift symmetry is present. Given our results, we consider a particular theory and demonstrate how the presence of symmetries provides integrability for the given black hole solution. We then find the charged extension of the solution thanks to the conformal invariance of the Maxwell action.