Light echos and coherent autocorrelations in a black hole spacetime

The Event Horizon Telescope recently produced the first images of a black hole. These images were synthesized by measuring the coherent correlation function of the complex electric field measured at telescopes located across the Earth. This correlation function corresponds to the Fourier transform of the image under the assumption that the source emits spatially incoherent radiation. However, black holes differ from standard astrophysical objects: in the absence of absorption and scattering, an observer sees a series of increasingly demagnified echos of each emitting location. These echos correspond to rays that orbit the black hole one or more times before reaching the observer. This multi-path propagation introduces spatial and temporal correlations into the electric field that encode properties of the black hole, irrespective of intrinsic variability. We explore the coherent temporal autocorrelation function measured at a single telescope. Specifically, we study the simplified toy problem of scalar field correlation functions ⟨psi(t)psi(0)⟩ sourced by fluctuating matter located near a Schwarzschild black hole. We find that the correlation function is peaked at times equal to integer multiples of the photon orbit period; the corresponding power spectral density vanishes like lambda/r (g) where r (g) = GM/c (2) is the gravitational radius of the black hole and lambda is the wavelength of radiation observed. For supermassive black holes observed at millimeter wavelengths, the power in echos is suppressed relative to direct emission by similar to 10(-13) lambda (mm)/M (6), where lambda (mm) = lambda/(1 mm) and M (6) = M/(10(6) M (circle dot)). Consequently, detecting multi-path propagation near a black hole using the coherent electric field autocorrelation is infeasible with current technology.

Automated summary

The Event Horizon Telescope has produced the first images of a black hole by synthesizing complex electric field measurements from telescopes across the Earth. However, the unique properties of black holes, including multiple path propagation introducing spatial and temporal correlations, make it currently infeasible to detect multi-path propagation near a black hole using the coherent electric field autocorrelation.