  The fast variability of energetic TeV photons from the center of M87 has been
detected, offering a new clue to estimate spins of supermassive black holes
(SMBHs). We extend the study of Wang et al. (2008) by including all of general
relativistic effects. We numerically solve the full set of relativistic
hydrodynamical equations of the radiatively inefficient accretion flows (RIAFs)
and then obtain the radiation fields around the black hole. The optical depth
of the radiation fields to TeV photons due to pair productions are calculated
in the Kerr metric. We find that the optical depth strongly depends on: (1)
accretion rates as $\tautev\propto \dot{M}^{2.5-5.0}$; (2) black hole spins;
and (3) location of the TeV source. Jointly considering the optical depth and
the spectral energy distribution radiated from the RIAFs, the strong
degeneration of the spin with the other free parameters in the RIAF model can
be largely relaxed. We apply the present model to M87, wherein the RIAFs are
expected to be at work, and find that the minimum specific angular momentum of
the hole is $a\sim0.8$. The present methodology is applicable to M87-like
sources with future detection of TeV emissions to constrain the spins of SMBHs.
