Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field

TL;DR

This paper develops higher-derivative gravity theories coupled with non-minimal Maxwell fields, constructs exact black hole solutions, and explores thermodynamics and holographic properties, revealing novel insights into their physical behavior.

Contribution

It introduces a new class of higher-derivative gravities with second-order equations of motion for metric and gauge fields, and constructs exact black hole solutions within this framework.

Findings

Exact magnetically-charged black holes in four dimensions

Exact electrically-charged Lifshitz black holes with z=2

Discrepancy between thermodynamics from Wald and Euclidean methods

Abstract

We construct higher-derivative gravities with a non-minimally coupled Maxwell field. The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion are second order for both the metric and the Maxwell potential. We also generalize the construction to involve a generic non-minimally coupled $p$-form field strength. We then focus on one low-lying example in four dimensions and construct the exact magnetically-charged black holes. We also construct exact electrically-charged $z=2$ Lifshitz black holes. We obtain approximate dyonic black holes for the small coupling constant or small charges. We find that the thermodynamics based on the Wald formalism disagrees with that derived from the Euclidean action procedure, suggesting this may be a general situation in higher-derivative gravities with non-minimally coupled form fields. As an application in the AdS/CFT correspondence, we study the entropy/viscosity ratio for the AdS or Lifshitz planar black holes, and find that the exact ratio can be obtained without having to know the details of the solutions, even for this higher-derivative theory.