We present the results from a detailed X-ray variability analysis of 66 AGN in the Lockman Hole, which have optical spectroscopic identifications. We compare, quantitatively, their variability properties with the properties of local AGN, and we study
the variability-luminosity relation as a function of redshift, and the variability-redshift relation in two luminosity bins. We use archival data from the last 10 XMM observations of the Lockman Hole field to extract light curves in the rest frame, 2-10 keV band. We use the normalized excess variance to quantify the variability amplitude. Using the latest results regarding the AGN power spectral shape and its dependence on black hole mass and accretion rate, we are able to compute model variability-luminosity curves, which we compare with the relations we observe. When we consider all the sources in our sample, we find that their variability amplitude decreases with increasing redshift and luminosity. These global anti-correlations are less pronounced when we split the objects in various luminosity and redshift bins. We do not find a significant correlation between variability amplitude and spectral slope. The variability-luminosity relation that we detect has a larger amplitude when compared to that of local AGN. We also find that, at a given luminosity, the variability amplitude increases with redshift up to z~1, and then stays roughly constant. Our results imply that the AGN X-ray mechanism operates in the same way at all redshifts. Among objects with the same luminosity in our sample, the black hole mass decreases and the accretion rate increases with larger redshift.
