X-ray Probes of Black Hole Accretion Disks for Testing the No-Hair Theorem
The spins of a number of supermassive and stellar-mass black holes have been measured based on detections of thermal continuum emission and relativistically broadened iron lines in their x-ray spectra. Likewise, quasiperiodic variability has been observed in several sources. Such measurements commonly make the assumption that black holes are described by the Kerr metric, which according to the no-hair theorem characterizes black holes uniquely in terms of their masses and spins. This fundamental property of black holes can be tested observationally by measuring potential deviations from the Kerr metric introduced by a parametrically deformed Kerr-like spacetime. Thermal spectra, iron lines, and variability have already been studied extensively in several such metrics, which usually depend on only one particular type of deviation or contain unphysical regions outside of the compact object. In this paper, I study these x-ray probes in the background of a new Kerr-like metric which depends on four independent deviation functions and is free of pathological regions outside of the event horizon. I show that the observed signals depend significantly on primarily two types of deviations and that the strong correlation between the spin and the deviation parameters found previously in other Kerr-like metrics is partially broken for rapidly spinning black holes. This suggests that high-spin sources are the best candidates for tests of the no-hair theorem with x-rays and I obtain first constraints on such deviations from the stellar-mass black hole Cygnus X-1.