The Sound of an Orbit: A Quantum Spectrum at the ISCO

Abstract

The quantum signature of the innermost stable circular orbit (ISCO), a region of profound importance in black hole astrophysics, is investigated. An atom is modeled as an Unruh-DeWitt detector coupled to a massless scalar field in the Boulware vacuum, and the excitation rate is calculated for a detector following a circular geodesic at the ISCO of a Schwarzschild black hole. In stark contrast to the continuous thermal spectra associated with static or infalling observers, the analysis reveals a unique, non-thermal excitation spectrum characterized by a discrete frequency comb of sharp, resonant peaks. The locations of these peaks are determined by the orbital frequency at the ISCO, while their intensity increases dramatically as the orbit approaches this final stability boundary. This distinct spectral signature offers a novel theoretical probe of the quantum vacuum in a strong-field gravitational regime and provides a clear distinction between the quantum phenomena experienced by observers on different trajectories. The findings have potential implications for interpreting the emission spectra from accretion disks and open new avenues for exploring the connection between quantum mechanics and gravity.