https://doi.org/10.1140/epjc/s10052-022-10155-w
Regular Article - Theoretical Physics
Quasinormal modes in two-photon autocorrelation and the geometric-optics approximation
1
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
2
Escola de Engenharia de Lorena, Universidade de São Paulo, 12602-810, Lorena, SP, Brazil
3
Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology, 310032, Hangzhou, China
4
Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, 430074, Wuhan, China
5
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, Shanghai, China
Received:
2
November
2021
Accepted:
20
February
2022
Published online:
1
March
2022
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.
© The Author(s) 2022
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