6. Black hole shadow drift and photon ring frequency drift

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Context: Together with Leonardo Giani and Tays Miranda, I recently led a study that demonstrates how redshift drifts alter the apparent angular diameter of black holes’ shadows and the frequency of their photon rings over time in a McVittie spacetime. This particular spacetime model replicates the behavior of Schwarzschild black holes at small scales and the Friedmann-Lemaître-Robertson-Walker metric at large scales. By applying this technique, we not only placed limits on the gravitational coupling but also on the maximum accretion rate of supermassive black holes.

Method: In McVittie, the angular diameter of a shadow is intimately tied to its Schwarzschild radius and angular diameter distance. I computed the relative changes in the shadow’s size over time based on the black hole mass (M) and distance (G) functions of time. Subsequently, I used data from the Event Horizon Telescope to test M87* while initially assuming a stationary black hole in general relativity, therefore determining the effect of dark energy on the shadow. After eliminating the assumption of stationarity, I established a threshold for the variation in G and M. Ultimately, I expanded my research to include photon rings, which, in the future, should provide more precise measurements.

Results:

• Through this methodology, I found that redshift drifts presented a limit on the relative temporal changes to the gravitational coupling of approximately \(10^{-3} - 10^{-4}\) per year using data from the EHT’s M87*.
• Upon the presumption that General Relativity is the correct gravitational theory, I concluded that the shadows and photon rings offer insight into M87*’s maximum accretion rate, approximated at a rate of about \(10^5 M_{\odot}\) per year.