  We present new calculations of X-ray polarization from black hole (BH)
accretion disks in the thermally-dominated state, using a Monte-Carlo
ray-tracing code in full general relativity. In contrast to many previously
published studies, our approach allows us to include returning radiation that
is deflected by the strong-field gravity of the BH and scatters off of the disk
before reaching a distant observer. Although carrying a relatively small
fraction of the total observed flux, the scattered radiation tends to be highly
polarized and in a direction perpendicular to the direct radiation. For
moderately large spin parameters (a/M >~ 0.9), this scattered returning
radiation dominates the polarization signal at energies above the thermal peak,
giving a net rotation in the polarization angle of 90 deg. We show how these
new features of the polarization spectra from BHs in the thermal state may be
developed into a powerful tool for measuring BH spin and probing the gas flow
in the innermost disk. In addition to determining the emission profile,
polarization observations can be used to constrain other properties of the
system such as BH mass, inclination, and distance. New instruments currently
under development should be able to exploit this tool in the near future.
