  We present a model of gamma-ray emission through neutral pion production and
decay in two-temperature accretion flows around supermassive black holes. We
refine previous studies of such a hadronic gamma-ray emission by taking into
account (1) relativistic effects in the photon transfer and (2) absorption of
gamma-ray photons in the radiation field of the flow. We use a fully general
relativistic description of both the radiative and hydrodynamic processes,
which allows us to study the dependence on the black hole spin. The spin value
strongly affects the gamma-ray emissivity within ~10 gravitational radii. The
central regions of flows with the total luminosities L < 0.001 of the Eddington
luminosity are mostly transparent to photons with energies below 10 GeV,
permitting investigation of the effects of space-time metric. For such L, an
observational upper limit on the gamma-ray (0.1-10 GeV) to X-ray (2-10 keV)
luminosity ratio of L_{0.1-10 GeV}/L_{2-10 keV} << 0.1 can rule out rapid
rotation of the black hole; on the other hand, a measurement of L_{0.1-10
GeV}/L_{2-10 keV} ~ 0.1 cannot be regarded as the evidence of rapid rotation,
as such a ratio can also result from a flat radial profile of gamma-ray
emissivity (which would occur for nonthermal acceleration of protons in the
whole body of the flow). At L > 0.01 of the Eddington luminosity, the gamma-ray
emission from the innermost region is strongly absorbed and the observed
gamma-rays do not carry information on the value of the black hole spin. We
note that if the X-ray emission observed in Centaurus A comes from an accretion
flow, the hadronic gamma-ray emission from the flow should contribute
significantly to the MeV/GeV emission observed from the core of this object,
unless it contains a slowly rotating black hole and protons in the flow are
thermal.
