On Black Hole Stability in Critical Gravities

TL;DR

This paper studies the stability of AdS black holes in extended gravity theories with higher curvature terms, analyzing mode spectra and boundary conditions at the critical point to determine stability conditions.

Contribution

It provides a linearized analysis of black hole perturbations in critical gravities, identifying the role of log modes and boundary conditions in stability.

Findings

No exponentially-growing tachyon modes in black holes.

Massless spin-2 modes have zero energy at the critical point.

Stability depends on truncating negative-energy log modes via boundary conditions.

Abstract

We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive spin-2 modes are replaced by the log modes. There always exist certain linear combination of massless and log modes that has negative energy. Thus the stability of the black holes requires that the log modes to be truncated out by the boundary condition.