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The spins of a number of supermassive and stellar-mass black holes have beenmeasured based on detections of thermal continuum emission and relativisticallybroadened iron lines in their x-ray spectra. Likewise, quasiperiodicvariability has been observed in several sources. Such measurements commonlymake the assumption that black holes are described by the Kerr metric, whichaccording to the no-hair theorem characterizes black holes uniquely in terms oftheir masses and spins. This fundamental property of black holes can be testedobservationally by measuring potential deviations from the Kerr metricintroduced by a parametrically deformed Kerr-like spacetime. Thermal spectra,iron lines, and variability have already been studied extensively in severalsuch metrics, which usually depend on only one particular type of deviation orcontain unphysical regions outside of the compact object. In this paper, Istudy these x-ray probes in the background of a new Kerr-like metric whichdepends on four independent deviation functions and is free of pathologicalregions outside of the event horizon. I show that the observed signals dependsignificantly on primarily two types of deviations and that the strongcorrelation between the spin and the deviation parameters found previously inother Kerr-like metrics is partially broken for rapidly spinning black holes.This suggests that high-spin sources are the best candidates for tests of theno-hair theorem with x-rays and I obtain first constraints on such deviationsfrom the stellar-mass black hole Cygnus X-1.

X-ray Probes of Black Hole Accretion Disks for Testing the No-Hair Theorem