We present a general relativistic accretion disc model and its application to the soft-state X-ray spectra of black hole binaries .
The model assumes a flat , optically thick disc around a rotating Kerr black hole .
The disc locally radiates away the dissipated energy as a blackbody .
Special and general relativistic effects influencing photons emitted by the disc are taken into account .
The emerging spectrum , as seen by a distant observer , is parametrized by the black hole mass and spin , the accretion rate , the disc inclination angle and the inner disc radius .

We fit the ASCA soft state X-ray spectra of LMC X-1 and GRO J1655–40 by this model .
We find that having additional limits on the black hole mass and inclination angle from optical/UV observations , we can constrain the black hole spin from X-ray data .
In LMC X-1 the constrain is weak , we can only rule out the maximally rotating black hole .
In GRO J1655–40 we can limit the spin much better , and we find 0.68 \leq a \leq 0.88 .
Accretion discs in both sources are radiation pressure dominated .
We don ’ t find Compton reflection features in the spectra of any of these objects .