No Scalar-Haired Cauchy Horizon Theorem in Einstein-Maxwell-Horndeski Theories

TL;DR

This paper extends a no inner horizon theorem to Einstein-Maxwell-Horndeski theories, analyzing black hole interiors and showing the presence of curvature singularities where mass extremizes and temperature vanishes.

Contribution

It generalizes the no Cauchy horizon theorem to a broader class of scalar-tensor theories, including Horndeski models, and explores their interior geometries.

Findings

Black hole interiors feature a space-like curvature singularity.

Mass extremum coincides with vanishing Hawking temperature.

The theorem extends to general Horndeski theories via disformal transformations.

Abstract

Recently, a no inner (Cauchy) horizon theorem for static black holes with non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories. In this paper, we extend the theorem to the static black holes in Einstein-Maxwell-Horndeski theories. We study the black hole interior geometry for some exact solutions and find that the spacetime has a (space-like) curvature singularity where the black hole mass gets an extremum and the Hawking temperature vanishes. We discuss further extensions of the theorem, including general Horndeski theories from disformal transformations.