About the ability of agnostic X-ray tests of the Kerr Hypothesis to discover new physics

In the past decade, we have seen an unprecedented progress in our ability of testing general relativity in the strong field regime with black hole observations. Most studies have focused on the so-called tests of the Kerr hypothesis: they have tried to verify whether the spacetime geometry around black holes is described by the Kerr solution as expected in general relativity. One can follow either a theory-specific analysis or an agnostic approach. Each strategy has its advantages and disadvantages. In this work, we study the ability of agnostic X-ray tests of the Kerr hypothesis to discover new physics. We simulate X-ray observations of bright Galactic black holes of specific theories of gravity and we analyze the simulated data with a reflection model employing the correct theory of gravity and another reflection model for agnostic tests of the Kerr hypothesis. Our results suggest that agnostic X-ray tests are valid tools to discover new physics, but their constraining power may be lower than a theory-specific analysis.