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

TL;DR

This paper investigates black hole light echoes through two-photon autocorrelation, linking time-domain phenomena with quasinormal modes and geometric optics, and demonstrates numerical results for Schwarzschild and Kerr black holes.

Contribution

It establishes a connection between light echoes, quasinormal modes, and geometric optics, providing a new analytical framework and numerical analysis for Schwarzschild and Kerr black holes.

Findings

Light echoes arise from collective effects of quasinormal modes.

Dominant contributions are from the eikonal limit, consistent with geometric optics.

Potential differences in light echoes between geometric optics and perturbation theory for Kerr black holes.

Abstract

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