Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

TL;DR

This work develops a generalised Kaluza–Klein reduction of a truncated Lovelock (Gauss–Bonnet) gravity theory with Maxwell fields to obtain a second-order, higher-derivative scalar–vector–tensor theory, controlled by a real parameter $\delta$. The authors construct exact static black-hole solutions in the reduced theory, including planar and curved horizons, both in Einstein and Galileon frames, and analyze how higher-derivative corrections dress naked singularities and alter horizon structure. They formulate a holographic dictionary for toroidal reductions, compute the thermodynamics, and derive first-order hydrodynamics (notably $\eta/s$ and Buchel bounds) in the reduced theory, illustrating consistency with higher-dimensional scale-invariant behavior. They also extend the analysis to non-diagonal reductions, obtaining boosted planar GB black holes with a corresponding holographic description. Overall, the paper links higher-derivative gravity, Galileon theories, and holography to produce analytically tractable black-hole solutions and transport properties with potential applications in modified gravity and holographic matter systems.

Abstract

We consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory, depends on a single real parameter and yields second-order field equations. Due to the presence of higher-derivative terms, the theory has multiple applications in modifications of Einstein gravity (Galileon/Horndesky theory) and holography (Einstein-Maxwell-Dilaton theories). We find and analyze charged black hole solutions with planar or curved horizons, both in the 'Einstein' and 'Galileon' frame, with or without cosmological constant. Naked singularities are dressed by a geometric event horizon originating from the higher-derivative terms. The near-horizon region of the near-extremal black hole is unaffected by the presence of the higher derivatives, whether scale invariant or hyperscaling violating. In the latter case, the area law for the entanglement entropy is violated logarithmically, as expected in the presence of a Fermi surface. For negative cosmological constant and planar horizons, thermodynamics and first-order hydrodynamics are derived: the shear viscosity to entropy density ratio does not depend on temperature, as expected from the higher-dimensional scale invariance.