Testing conformal gravity with the supermassive black hole in 1H0707-495

Recently, two of us have found a family of singularity-free rotating black hole solutions in Einstein's conformal gravity. These spacetimes are characterized by three parameters: the black hole mass M, the black hole spin angular momentum J, and a parameter L that is not specified by the theory but can be expected to be proportional to the black hole mass M. The Kerr black hole solution of Einstein's gravity is recovered for L = 0. In a previous paper, we showed that X-ray data of astrophysical black holes require L= M < 1.2. In the present paper, we report the results of a more sophisticated analysis. We apply the X-ray reflection model RELXILL_NK to NuSTAR and Swift data of the supermassive black hole in 1H0707-495. We find the constraint L=M < 0.45 (90% confidence level).