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We calculate the structure of a standard accretion disk with coronasurrounding a massive Kerr black hole in general relativistic frame, in whichthe corona is assumed to be heated by the reconnection of the strongly buoyantmagnetic fields generated in the cold accretion disk. The emergent spectra ofthe accretion disk-corona systems are calculated by using the relativisticray-tracing method. We propose a new method to calculate the emergentComptonized spectra from the coronae. The spectra of the disk-corona systemswith a modified $\alpha$-magnetic stress show that both the hard X-ray spectralindex and the hard X-ray bolometric correction factor $L_{\rm bol}/L_{\rmX,2-10keV}$ increase with the dimensionless mass accretion rate, which arequalitatively consistent with the observations of active galactic nuclei(AGNs). The fraction of the power dissipated in the corona decreases withincreasing black hole spin parameter $a$, which leads to lower electrontemperatures of the coronas for rapidly spinning black holes. The X-rayemission from the coronas surrounding rapidly spinning black holes becomes weakand soft. The ratio of the X-ray luminosity to the optical/UV luminosityincreases with the viewing angle, while the spectral shape in the X-ray band isinsensitive with the viewing angle. We find that the spectral index in theinfrared 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 thindisk model.

A general relativistic model of accretion disks with coronae surrounding Kerr black holes