Light rings and long-lived modes in quasi-black hole spacetimes

TL;DR

This paper investigates quasi-black hole spacetimes with light rings, demonstrating that such horizonless objects can have long-lived modes, which supports the idea that light rings are indicative of black holes.

Contribution

The study provides explicit calculations showing that horizonless spacetimes with light rings can be unstable, offering evidence that light rings are potential observational signatures of black holes.

Findings

Long-lived modes exist in quasi-black holes with light rings.

Light rings in horizonless spacetimes may indicate instability.

Light rings could serve as observational evidence for black holes.

Abstract

It has been argued that ultracompact objects, which possess light rings but no horizons, may be unstable against gravitational perturbations. To test this conjecture, we revisit the quasi-black hole solutions, a family of horizonless spacetimes whose limit is the extremal Reissner-Nordstr\"om black hole. We find a critical parameter at which the light rings just appear. We then calculate the quasinormal modes of the quasi-black holes. Both the WKB result and the numerical result show that long-live modes survive for the range where light rings exist, indicating that horizonless spacetimes with light rings are unstable. Our work provides a strong and explicit example that light rings could be direct observational evidence for black holes.