Photon ring autocorrelations from gravitational fluctuations around a black hole

The images of supermassive black holes in M87 and our galaxy captured by the Event Horizon Telescope (EHT) might open up a new way for exploring black hole physics at the horizon scale. Theoretically, this could provide insights into studying the emission sources around a black hole or the geometries of the black hole itself. This paper investigates the two-point correlations of intensity fluctuations on the photon ring, resulting from the existence of shock waves or gravitational fluctuations around a black hole. Following approaches used in the field of gravitational wave detectors, we introduce response functions of very long baseline interferometry (VLBI) for detecting gravitational fluctuations and study the shape of the overlap reduction functions. It is found that the shape of the correlations here differs from that resulting from stochastic emission sources. By providing an order-of-magnitude estimate for the signal-to-noise ratio (SNR), we obtain sensitivity curves for the detection of gravitational fluctuations. This might reveal the potential for detecting gravitational fluctuations with future VLBI observations in the LIGO frequency band.