Holographic Lovelock Gravities and Black Holes

TL;DR

This paper explores the holographic implications of Lovelock gravity theories in AdS spacetimes, analyzing black hole solutions, boundary correlators, and causality constraints to understand their dual CFT properties.

Contribution

It formulates existence conditions for AdS black holes in Lovelock gravity, computes holographic Weyl anomalies, and proposes a universal energy flux expression across dimensions.

Findings

Causality constraints restrict Lovelock parameters.

Holographic stress tensor correlators mimic supersymmetry relations.

Energy flux positivity aligns with causality conditions.

Abstract

We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition for asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on Lovelock parameters by demanding causality of the boundary theory. For the case of cubic Lovelock gravity in seven spacetime dimensions we compute the holographic Weyl anomaly and determine the three point functions of the stress energy tensor in the boundary CFT. Remarkably, these correlators happen to satisfy the same relation as the one imposed by supersymmetry. We then compute the energy flux; requiring it to be positive is shown to be completely equivalent to requiring causality of the finite temperature CFT dual to the black hole. These constraints are not stringent enough to place any positive lower bound on the value of viscosity. Finally, we conjecture an expression for the energy flux valid for any Lovelock theory in arbitrary dimensions.