One alternative to general relativity, called asymptotically safe gravity, is one of the better established routes to solving the difficult problem of devising a theory of quantum gravity (which is necessary to integrate general relativity with the Standard Model of Particle Physics).
This approach has a characteristic observable difference from general relativity: its black holes are smaller. But astronomy observations of actual black holes show that unmodified general relativity is a better fit than this alternative. So, this otherwise promising approach to quantum gravity may not be the right one.
According to the asymptotically safe gravity, black holes can have characteristics different from those described according to general relativity. Particularly, they are more compact, with a smaller event horizon, which in turn affects the other quantities dependent on it, like the photon ring and the size of the innermost stable circular orbit.
We decided to test the latter by searching in the literature for observational measurements of the emission from accretion disk around stellar-mass black holes. All published values of the radius of the inner accretion disk were made homogeneous by taking into account the most recent and more reliable values of mass, spin, viewing angle, and distance from the Earth. We do not find any significant deviation from the expectations of general relativity. Some doubtful cases can be easily understood as due to specific states of the object during the observation or instrumental biases.
Luigi Foschini, Alberto Vecchiato, Alfio Bonanno, "Searching for quantum-gravity footprint around stellar-mass black holes" arXiv:2411.09528 (November 14, 2024).
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