The lack of influence of the scalar hair on the DC conductivity

TL;DR

This paper demonstrates that scalar hair in beyond-Horndeski black hole solutions does not directly influence DC conductivity, highlighting the robustness of transport properties against scalar hair variations.

Contribution

It shows that scalar hair's effect on DC conductivity is only indirect, and this remains true even in more general beyond-Horndeski theories.

Findings

Scalar hair does not directly affect DC conductivity.

Transport properties depend only on horizon location, not hair parameter.

Results are consistent across different beyond-Horndeski models.

Abstract

Recently obtained black hole solutions within the framework of beyond-Horndeski theories, which have the advantage of featuring primary hair, are generalized in the presence of two axionic fields. In order to induce a momentum dissipation, the axionic field solutions are homogeneously distributed along the horizon coordinates of the planar base manifold. We show that, despite the explicit dependence of the scalar field and the metric on the primary hair, this latter does not directly affect the calculation of transport properties. Its influence is indirect, modifying the horizon location, but the transport properties themselves do not explicitly depend on the hair parameter. We take a step further and show that even within a more general class of beyond-Horndeski theories, where the scalar field depends linearly on the hair parameter, the scalar hair still has no direct impact on the DC conductivity. This result underscores the robustness of our earlier findings, and seem to confirm that the transport properties remain unaffected by the explicit presence of the hair parameter.