Quasinormal modes in two-photon autocorrelation and the geometric-optics approximation

In this work, we study the black hole light echoes in terms of two-photon autocorrelation and explore their connection with quasinormal modes. It is shown that above time-domain phenomenon can be analyzed by utilizing well-known frequency-domain relations between modes characteristic parameters null geodesics. We found correlator, obtained inverse Fourier transform, naturally acquires echo feature, which attributed to a collective effect asymptotic poles through weighted summation squared modulus relevant Green's functions. Specifically, contour integral leads taking over both overtone index angular momentum. Moreover, dominant contributions are from those eikonal limit, consistent existing findings using geometric-optics arguments. For Schwarzschild holes, demonstrate results numerically considering transient spherical source. Also, for Kerr spacetimes, point out potential difference resulting approach perturbation theory. Possible astrophysical implications present addressed.