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