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).