No asymptotically highly damped quasi-normal modes without horizons?

TL;DR

This paper investigates whether highly damped quasi-normal modes exist in horizonless spacetimes and finds they do not, supporting the idea that such modes are linked to the presence of horizons.

Contribution

It proves that asymptotically highly damped quasi-normal modes are absent in a broad class of horizonless, asymptotically flat spacetimes, strengthening the horizon-connection hypothesis.

Findings

Highly damped modes do not exist without horizons.

Supports the link between quasi-normal modes and horizon properties.

Provides evidence for the horizon-connection conjecture.

Abstract

We explore the question of what happens with the asymptotically highly damped quasi-normal modes ($\ell$ fixed, $|\omega_{I}|\to\infty$) when the underlying spacetime has no event horizons. We consider the characteristic oscillations of a scalar field in a large class of asymptotically flat spherically symmetric static spacetimes without (absolute) horizons, such that the class accommodates the cases that are known to be of some sort of physical interest. The question of the asymptotic quasi-normal modes in such spacetimes is relevant to elucidate the connection between the behavior of the asymptotic quasi-normal modes and the quantum properties of event horizons, as put forward in some recent important conjectures. We prove for a large class of asymptotically flat spacetimes without horizons that the scalar field asymptotically highly damped modes do not exist. This provides in our view additional evidence that there is indeed a close link between the asymptotically highly damped modes and the existence of spacetime horizons (and their properties).