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 autocorrelation function \xi ( T ) = \langle L ( t ) L ( t - T ) \rangle .
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 _ { \ast } ,a ) and magnification \mu _ { j } ( r _ { \ast } ,a ) of the j th path ( j = 1 , 2 , 3 , \ldots ) , relative to the primary path ( j = 0 ) , as a function of the emission radius r _ { \ast } and black hole spin 0 \leq a / M \leq 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 \approx 0.853 ) , the j = 1 , 2 , 3 fluxes are , respectively , 27 \% , 2 \% and 0.1 \% of the j = 0 flux .