Active Galactic Nuclei as probes of Relativistic Thermodynamics.

More than 110 years after the introduction of Special Relativity, Relativistic Thermodynamics (hereafter RT) has not yet been put on firm grounds. The issue is often exemplified by the question concerning how the temperature of a moving body having a rest frame temperature $T_{0}$ transforms with the observed body's speed: will temperature transform linearly with the Lorentz factor or its inverse, $i.e.$, will a moving body appear hotter or colder (see Ott, 1963 and Einstein, 1907)? Or instead is temperature a relativistic invariant (Landsberg, 1968)? Within an astrophysical context the environment of Active Galactic Nuclei (AGNs) provides two ideal sites where matter moves at relativistic velocities and thus RT could be probed: the plunging region of an accretion disc, beyond the Innermost Stable Circular Orbit, and the Interstellar/Intracluster Medium where the jet interacts with the cold, star-forming clouds. We compare the predictions from different recently proposed RT theoretical models concerning different emission lines and properties, demonstrating how one could exploit AGNs and their relativistic jets as probes of RT, one of the last open issues in Relativity.