The hard X-ray emission observed in accreting compact sources is believed to be produced by inverse Compton scattering of soft photons arising from the accretion disc by energetic electrons thermally distributed above the disc, the so-called X-ray corona. Many independent observations suggest that such coronae should be compact and located very close to the black hole. In this case general relativistic (GR) effects should play an important role to the continuum X-ray emission from these sources, and in particular in the observed high energy cut-off, which is a measure of the intrinsic temperature of the corona. Our results show that the energy shift between the observed and intrinsic high energy cut-off due to GR effects can be as large as 2 - 8 times, depending on the geometry and size of the corona as well as its inclination. We provide estimates of this energy shift in the case of a lamp-post and a flat, rotating corona, around a Kerr and a Schwartzschild black hole, for various inclinations, and coronal sizes. These values could be useful to correct the observed high energy cut-off and/or coronal temperatures, either in the case of individual or large sample of objects.
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