Timing of echoes in electromagnetic radiation from hot spots orbiting a Kerr black hole impostor

Abstract We investigate the light curve of an isolated bright spot in a Keplerian orbit around a Kerr black hole candidate to probe possible deviations from the standard event-horizon picture. In particular, we explore the presence of a reflective surface, namely a “mirror” near the horizon, and its observable consequences. We present estimates on the time delays of the echoes of electromagnetic radiation from the mirror or some other reflecting area related to black hole mimickers. Our results show that photon reflections from such a surface imprint distinct late-time features in the light curve, producing an electromagnetic analogue of gravitational wave echoes. For lower values of the spin, the reflected signal appears within the same orbital period and leads to a noticeable enhancement of the flux. In contrast, for higher spins, the effect emerges only after several orbits, giving rise to a characteristic echo-wave train. These features provide a potential observational signature of horizon-scale modifications in compact objects.