Exploring the black hole spectrum of axionic Horndeski theory

TL;DR

This paper introduces an efficient algorithm to find exact black hole solutions in a generalized Einstein-Maxwell-Horndeski theory with axion fields, revealing new asymptotic behaviors and implications for dual field theories.

Contribution

The authors develop a systematic method to derive exact black hole solutions in Horndeski theories with axions, including novel asymptotically AdS and Lifshitz black holes, and analyze their IR fixed points.

Findings

Derived new asymptotically AdS black holes with extremal limits flowing to AdS2×R2.

Discovered asymptotically Lifshitz black holes with dynamical exponent z>1.

Analyzed DC transport properties relevant for condensed matter applications.

Abstract

We provide a ``user-friendly'' algorithm to systematically and rapidly obtain exact planar black hole solutions in the Einstein-Maxwell theory deformed by the most general shift- and reflection-symmetric Horndeski sector where the usual Galileon is replaced by a tuple of scalars with profiles linear in the coordinates of the transverse manifold. Under precise assumptions, these axion backgrounds break the translational invariance of the system, causing momentum dissipation in the holographically dual field theory. The success of the method relies on the simple realization that the bulk equations of motion become more tractable when written in terms of the axions kinetic terms, instead of the radial coordinate. Showcasing this particularly efficient recipe, we derive novel asymptotically AdS black holes, and show that their extremal counterparts always flow to an $\mathrm{AdS}_2\times \mathbb{R}^2$ infrared fixed point. Additionally, we report an interesting family of new asymptotically Lifshitz black hole solutions with $z>1$. Finally, we discuss the DC transport properties of the dual relativistic field theories in view of possible applications to condensed matter systems.