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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.
Highlights
It is noted that the above approaches are essentially based on the properties of the null geodesics
The specific relations between the quasinormal modes of field perturbations and the characteristic parameters of the corresponding null geodesics have been extensively studied in the literature [9]
We argue that the resultant light echoes in the time domain can be attributed to a collective effect of the low-lying asymptotic quasinormal modes at the eikonal limit
Summary
While the black hole shadow determines the spatially asymptotic boundary of increasingly demagnified subrings, the notion of FPO gives rise to another intriguing feature in the time domain, known as light echo or glimmer. At such a limit, the typical scale of spatial variation of the wavefront, roughly the size of the black hole, is more significant than the wavelength [6,7] In this regard, the light echo signature derived using the properties of null geodesics is not expected to comprise any information that does not survive the geometric-optics approximation. The resulting autocorrelations based on the null geodesics must be entirely irrelevant to the number of nodes of the waveform in the latitudinal direction In this context, from the perspective of the black hole perturbation theory, one might argue that it seems more appropriate to calculate the correlation function in terms of fields rather than light rays. Light echoes were observed in terms of the peaks attained at times equal to integer multiples of the photon orbit period These results are physically significant and consistent with the existing geometric-optic analysis. The last section is devoted to further discussions and concluding remarks
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