Black Hole Olympics: Metric Selection from the Event Horizon Telescope and LIGO-VIRGO Observations

We propose a new paradigm in the field of black hole physics, i.e., with more and more high precision observations, one must make a metric selection to determine which black hole is observationally preferred. In light of the shadow imaging data from the Event Horizon Telescope and gravitational wave measurements from the LIGO-VIRGO collaboration, we attempt to address this issue. Although not finding any obvious preference for a specific black hole metric based on current data, as a presentation of this new research paradigm, we rank these black hole metrics using the Bayesian information criterion. We find that Kerr and Reissner-Nordstr\"{o}m tie the first place in the black hole Olympics Games. Interestingly, we give the $2\,\sigma$ upper bound of the average electronic charge $Q<2.82\times10^{18}$ C for the Reissner-Nordstr\"{o}m spacetime, and the $2\,\sigma$ constraint on the average spin parameter $a=-0.02^{+4.07}_{-4.04}$ m for the Kerr spacetime, which is consistent with the prediction of zero rotation for a distant observer. Future multi-messenger and multi-wavelength observations will enhance the application of this new paradigm into tests of gravitational theories and black holes.