  Stellar-mass black holes offer what is perhaps the best scenario to test
theories of gravity in the strong-field regime. In particular, f(R) theories,
which have been widely discuss in a cosmological context, can be constrained
through realistic astrophysical models of phenomena around black holes. We aim
at building radiative models of thin accretion disks for both Schwarzschild and
Kerr black holes in f(R) gravity. We study particle motion in
f(R)-Schwarzschild and Kerr space-times. We present the spectral energy
distribution of the accretion disk around constant Ricci scalar f(R) black
holes, and constrain specific f(R) prescriptions using features of these
systems. A precise determination of both the spin and accretion rate onto black
holes along with X-ray observations of their thermal spectrum might allow to
identify deviations of gravity from General Relativity. We use recent data on
the high-mass X-ray binary Cygnus X-1 to restrict the values of the parameters
of a class of f(R) models.
