Testing conformal gravity with astrophysical black holes

Weyl conformal symmetry can solve the problem the spacetime singularities present in Einstein's gravity. In a recent paper, two of us have found a singularity-free rotating black hole solution in conformal gravity. In addition to the mass M and the spin angular momentum J of the black hole, the new solution has a new parameter, L, which here we consider to be proportional to the black hole mass. Since the solution is conformally equivalent to the Kerr metric, photon trajectories are unchanged, while the structure of an accretion disk around a black hole is affected by the value of the parameter L. In this paper, we show that x-ray data of astrophysical black holes require L/M < 1.2.