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Black holes in General Relativity are known as Kerr black holes and arecharacterized solely by two parameters, the mass $M$ and the spin $J$. All thehigher multipole moments of the gravitational field are functions of these twoparameters. For instance, the quadrupole moment is $Q=-J^2/M$, which impliesthat a measurement of $M$, $J$, and $Q$ for black hole candidates would allowone to test whether these objects are really black holes as described byGeneral Relativity. While future gravitational-wave experiments will be able totest the Kerr nature of these objects with very high accuracy, in this paper weshow that it is possible to put constraints on the quadrupole moment ofstellar-mass black hole candidates by using presently available X-ray data ofthe thermal spectrum of their accretion disk.

Constraining the quadrupole moment of stellar-mass black-hole candidates with the continuum fitting method