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

TL;DR

This paper derives a consistent higher-derivative scalar-tensor theory from Lovelock gravity, explores black hole solutions, and investigates implications for holography and modifications of Einstein gravity, including thermodynamics and entanglement entropy.

Contribution

It introduces a new class of second-order scalar-tensor theories from Kaluza-Klein reduction of Lovelock gravity, with applications to black holes and holography.

Findings

Charged black hole solutions with various horizons are found and analyzed.

Naked singularities are cloaked by higher-derivative induced horizons.

The shear viscosity to entropy density ratio remains constant regardless of temperature.

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.