Light rings and long-lived modes in quasiblack hole spacetimes

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 quasiblack 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 quasiblack holes. Both the WKB result and the numerical result show that long-lived 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.