Since their discovery almost one century ago extragalactic jets have been puzzling astronomers. Inferred velocities close to the speed of light and high resolution, interferometric observations at radio frequencies suggest that these jets (in fact, beams of hot, tenuous plasma) are formed in the vicinity of the event horizon of a supermassive black hole at the core of some .galaxies. From this small scale (of the order of the size of the solar system) extragalactic jets propagate without disruption along nine decades in distance scale well outside the host galaxy. Current theoretical models assume that the process of accretion from an orbiting disk around the central black hole provides the primary source of energy to power the jets which are further collimated and accelerated via magnetohydrodynamic processes up to highly relativistic speeds. In the introduction of the talk we shall review the observational status as well as the theoretical models that give support to our present understanding of the jet phenomenon. Despite the years of intensive research, many basic questions regarding the physics of jets as the formation mechanisms, the jet composition, the role of magnetic fields in the jet dynamics, or their remarkable stability, are still standing. One decade ago, the numerical simulation of relativistic jets was made possible thanks to the extension of high-resolution shock-capturing techniques to the relativistic regime. These techniques allowed for the first time to solve the equations of relativistic hydrodynamics under the extreme conditions (i.e., large flow Lorentz factors and strong shocks) found in this scenario. One of the aims of the talk will be to review the recent advances in numerical relativistic hydrodynamics and magnetohydrodynamics. Present simulations of jets cover all the relevant scales from the subparsec scale, at which jets are formed, and that remain unaffordable’to observations, up to the megaparsec scale. The role played by relativistic hydrodynamical simulations in the study of extragalactic jets, their success in interpreting the overall structure, dynamics and appearance of these objects, but also the difficulties to probe their physical conditions, will be the subject of the last part of the talk.
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