Conformal Boundary Conditions and Higher Curvature Gravity

TL;DR

This paper explores Einstein-Gauss-Bonnet gravity with conformal boundary conditions, analyzing boundary dynamics and thermodynamic behavior in Euclidean and Lorentzian signatures, revealing universal features in flat space limits.

Contribution

It introduces a systematic study of higher curvature boundary conditions, extending conformal boundary conditions to Einstein-Gauss-Bonnet gravity and analyzing their effects on black hole thermodynamics and boundary dynamics.

Findings

Entropy at high temperatures behaves like a lower-dimensional conformal field theory.

Higher curvature corrections are negligible in the flat space high-temperature limit.

Boundary Weyl factor dynamics are analyzed in black hole backgrounds.

Abstract

We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the extrinsic curvature is also fixed at the boundary. Here we generalize this boundary condition with the appropriate higher curvature correction. We study the problem both in Euclidean and Lorentzian signature. In Euclidean signature, we show that, similarly to the Einstein gravity case, the entropy at large temperatures exhibits the behavior of a conformal field theory in one lower dimension. We also show that in the flat space limit, the higher curvature corrections do not contribute to the leading behavior at high temperatures. We conjecture that this result is a universal feature of the flat space limit in the presence of conformal boundaries. We test our conjecture by analyzing charged black holes. In Lorentzian signature, we analyze the dynamics of the boundary Weyl factor in black hole backgrounds at the linearized level.