Thermal Origin of Black Hole Quasinormal Modes

Abstract

When a black hole rings after a merger, it emits gravitational waves at characteristic frequencies known as quasinormal modes (QNMs). In the eikonal limit, these modes are governed by the unstable circular light orbits that form the photon ring. In this work, we demonstrate that the ringing of a black hole has a precise thermal interpretation. A probe string propagating in the near-ring geometry acquires an induced Rindler horizon on its worldsheet, with a temperature set by the Lyapunov exponent of the photon ring. Out of this structure, the black hole QNMs emerge as thermal excitations, so that the characteristic ringing of a black hole is the retarded response of a thermal system living on the photon ring. We explicitly derive the QNM spectrum from two complementary perspectives: microscopically, via unstable transverse worldsheet fluctuations, and macroscopically, through the pole structure of the causal response function of an open thermal quantum system.