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The size and geometry of the X-ray emitting corona in AGNs are still not wellconstrained. Dov\v{c}iak & Done (2016) proposed a method based on calculationsassuming a point-like lamp-post corona. To perform more self-consistentcalculations of energy spectra of extended coronae, we develop monk, a MonteCarlo radiative transfer code dedicated to calculations of Comptonised spectrain the Kerr spacetime. In monk we assume Klein-Nishina scattering cross sectionand include all general relativistic effects. We find that for a corona locatedabove the disc, the spectrum is not isotropic, but with harder and lessluminous spectra towards observers at lower inclinations, owing to anisotropicillumination of the seed photons. This anisotropy also leads to anunderestimated size of the corona if we assume the corona to be a point-like,isotropic source located on the black hole rotation axis, demonstrating thenecessity of more self-consistent calculations. We also inspect the effect ofmotion and geometry of the corona on the emergent spectrum. Finally, we discussthe implication of anisotropic corona emission for the reflection spectrum inAGNs as well as black hole X-ray binaries (BHXRBs). We find that by assumingthe corona emission to be isotropic, one may underestimate the soft excess inAGNs and the reflection continuum and iron K fluorescent line flux in BHXRBs.

Constraining the size of the corona with fully relativistic calculations of spectra of extended corona. I - the Monte Carlo radiative transfer code