  We study low-mass binary X-ray sources involving stellar mass black holes
within massive gravity. Regarding the accretion disk, we adopt the standard
model for an optically thick, cool, and geometrically thin disk by
Shakura-Sunyaev. For the gravitational field generated by the black hole, we
consider the analogue of the Schwarzschild-de Sitter space-time of Einstein's
theory in massive gravity, for which we found an additional term linear in the
radial coordinate. Then, we compute the radial velocity, the energy density and
the pressure as a function of the radial coordinate, and the X-ray emission's
soft spectral component expected from the disk. We also investigated in
detailed the impact of this new geometry. Our result indicates that by using
observed spectra from confirmed X-ray binaries involving astrophysical black
holes, we can put strong constraints on alternative theories of gravity.
