Light Loop Echoes and Blinking Black Holes

Radiation emitted near a black hole reaches the observer by multiple paths; and when this radiation varies in time, the time-delays between the various paths generate a "blinking" effect in the observed light curve L(t) or its auto-correlation function xi(T)= <L(t)L(t-T)>. For the particularly important "face-on" configuration (in which the hole is viewed roughly along its spin axis, while the emission comes roughly from its equatorial plane -- e.g. from the inner edge of its accretion disk, or from the violent flash of a nearby/infalling star) we calculate the blinking in detail by computing the time delay Delta t_{j}(r,a) and magnification mu_{j}(r,a) of the jth path (j=1,2,3,...), relative to the primary path (j=0), as a function of the emission radius r and black hole spin 0<a/M<1. The particular geometry and symmetry of the nearly-face-on configuration enhances and "protects" the blinking signal, making it more detectable and more independent of certain astrophysical and observational details. The effect can be surprisingly strong: e.g. for radiation from the innermost stable circular orbit ("ISCO") of a black hole of critical spin (a_{crit}/M = 0.853), the j=1,2,3 fluxes are, respectively, 27%, 2% and 0.1% of the j=0 flux.