When a black hole rings after a merger it emits gravitational waves at fixed complex frequencies called quasinormal modes (QNMs). This paper argues that, in the short-wavelength limit, those ringing frequencies have a precise thermal origin. The authors show that a simple probe—an idealized string placed near the photon ring (the unstable circular light orbit around the hole)—develops an induced horizon on its two‑dimensional worldsheet. That induced horizon is Rindler‑like and comes with a temperature set by the photon ring’s instability, the Lyapunov exponent.

To reach this conclusion the researchers isolate the local geometry near the photon ring using a Penrose‑type limit. They then place a non‑backreacting probe string along the ring. The induced metric on the string’s worldsheet is Rindler, so the worldsheet state restricted to one Rindler wedge is thermal. Microscopically, unstable transverse vibrations of the string behave like an inverted harmonic oscillator. The outgoing resonances (so‑called Gamow modes) of that instability reproduce the familiar eikonal QNM spectrum: the real part comes from the light orbit frequency and the imaginary part (the damping) is proportional to the Lyapunov exponent, with a universal half‑integer offset in the overtone label.

The paper also gives a complementary, macroscopic picture. Treating the near‑ring system as an open thermal system whose excitations can leak away, they compute the causal response (the retarded Green’s function) restricted to the escape channel. General physical principles—causality, positivity of spectral weight, and the thermal Kubo–Martin–Schwinger property that characterizes equilibrium—force the resonance poles into the lower half of the complex frequency plane and fix the sign of the decay width. The universal half‑integer offset is given a geometric origin from the way Rindler boosts act on the escape coordinate.