A general relativistic model of accretion disks with coronae surrounding
  Kerr black holes
  We calculate the structure of a standard accretion disk with corona
surrounding a massive Kerr black hole in general relativistic frame, in which
the corona is assumed to be heated by the reconnection of the strongly buoyant
magnetic fields generated in the cold accretion disk. The emergent spectra of
the accretion disk-corona systems are calculated by using the relativistic
ray-tracing method. We propose a new method to calculate the emergent
Comptonized spectra from the coronae. The spectra of the disk-corona systems
with a modified $\alpha$-magnetic stress show that both the hard X-ray spectral
index and the hard X-ray bolometric correction factor $L_{\rm bol}/L_{\rm
X,2-10keV}$ increase with the dimensionless mass accretion rate, which are
qualitatively consistent with the observations of active galactic nuclei
(AGNs). The fraction of the power dissipated in the corona decreases with
increasing black hole spin parameter $a$, which leads to lower electron
temperatures of the coronas for rapidly spinning black holes. The X-ray
emission from the coronas surrounding rapidly spinning black holes becomes weak
and soft. The ratio of the X-ray luminosity to the optical/UV luminosity
increases with the viewing angle, while the spectral shape in the X-ray band is
insensitive with the viewing angle. We find that the spectral index in the
infrared waveband depends on the mass accretion rate and the black hole spin
$a$, which deviates from $f_\nu\propto\nu^{1/3}$ expected by the standard thin
disk model.
