A note on dilaton gravity with non-smooth potentials

TL;DR

This paper explores the effects of non-smooth potentials in dilaton gravity, analyzing delta-like contributions and solution ambiguities, and constructs exact solutions under static conditions relevant for brane world models.

Contribution

It introduces methods to handle non-smooth potentials in dilaton gravity, including delta-like sources and solution ambiguities, enabling analysis of brane world and point source models.

Findings

Explicit solutions for static non-smooth dilaton gravity models

Analysis of delta-like contributions on solutions

Framework for non-smooth dilaton gravity theories

Abstract

Recent interest in brane world models motivates the investigation of generic first order dilaton gravity actions, with potentials having some non-smoothness. We consider two different types of \delta-like contributions in the action and analyse their effects on the solutions. Furthermore a second source of non-smoothness arises due to the remaining ambiguities in the solutions in the separated smooth patches, after fixing all other constants by matching and asymptotic conditions. If moreover staticity is assumed, we explicitly construct exact solutions. With the methods described, for example models with point like sources or brane world models (where the second source of non-smoothness becomes crucial), can now be treated as non-smooth dilaton gravity theories.