How general is the strong cosmic censorship bound for quasinormal modes?

TL;DR

This paper investigates the universality of bounds on quasinormal modes of black holes across different gravity theories, showing that for small black holes, these bounds depend only on asymptotic parameters and not on near-horizon geometry.

Contribution

It provides numerical evidence that Hod's proposal and the strong cosmic censorship bound hold for small black holes in arbitrary metric theories, highlighting their universal behavior.

Findings

Bounds are satisfied for small black holes in various theories.

Quasinormal frequencies depend only on cosmological constant and mass.

Universal behavior of low-lying quasinormal modes in this regime.

Abstract

Hod's proposal claims that the least damped quasinormal mode of a black hole must have the imaginary part smaller than half of the surface gravity at the event horizon. The Strong Cosmic Censorship in General Relativity implies that this bound must be even weaker: half of the surface gravity at the Cauchy horizon. The appealing question is whether these bounds are limited by the Einstein theory only? Here we will present numerical evidence that once the black hole size is much smaller than then the radius of the cosmological horizon, both the Hod's proposal and the strong cosmic censorship bound for quasinormal modes are satisfied for general spherically symmetric black holes in an arbitrary metric theory of gravity. The low-lying quasinormal frequencies have the universal behavior in this regime and do not depend on the near-horizon geometry, but only on the asymptotic parameters: the value of the cosmological constant and black hole mass.