It has been suggested that X-ray observations of rapidly variable Seyfert galaxies may hold the key to probe the gas orbital motions in the innermost regions of accretion discs around black holes and, thus, trace flow patterns under the effect of the hole strong gravitational field. We explore this possibility analizing XMM-Newton observations of the seyfert 1 galaxy NGC 3783. A detiled time-resolved spectral analysis is performed down to the shortest possible time-scales (few ks) using excess maps and cross-correlating light curves in different energy bands. In addition to a constant core of the Fe K alpha line, we detected a variable and redshifted Fe K alpha emission feature between 5.3-6.1 keV. The line exhibits a modulation on a time-scale of 27 ks that is similar to and in phase with a modulation of the 0.3-10 keV source continuum. The time-scale of the correlated variability of the redshifted Fe line and continuum agrees with the local dynamical time-scale of the accretion disc at 10 r_g around a black hole of 10^7 M_sun. Given the shape of the redshfted line emission and the overall X-ray variability pattern, the line is likely to arise from the relativistic region near the black hole.
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