Variational principle for the relativistic hydrodynamic flows with discontinuities, and local invariants of motion. Abstract A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of discontinuities (including shocks) is presented in the framework of an exact Clebsch type representation of the four-velocity field as a...

In this paper, we calculate the relativistic bulk tensor and shear tensor of the relativistic accretion ows in the Kerr metric, overall and without any approximation. We obtain the relations of all components of the relativistic bulk and shear tensor in terms of components of four-velocity and its derivatives, Christoffel symbols and metric components in the BLF. Then, these components are deri...

The formation of singularities in relativistic flows is not well understood. Smooth solutions to the relativistic Euler equations are known to have a finite lifespan; the possible breakdown mechanisms are shock formation, violation of the subluminal conditions andmass concentration. We propose a new hybrid Glimm/centralupwind scheme for relativistic flows. The scheme is used to numerically inve...

The radiation we observe from blazars is most likely the product of the transformation of bulk kinetic energy into random energy. This process must have a relatively small efficiency (e.g. 10%) if jets are to power the extended radio–structures. Recent results suggest that the average power reaching the extended radio regions and lobes is of the same order of that produced by accretion and illu...

An abstract should be given Exact analytic solutions are derived for radiation in time-dependent relativistic flows. The flows are spherically-symmetric homologous explosions or implosions of matter with a grey extinction coefficient. The solutions are suitable for testing numerical transfer codes, and this is illustrated for a fully relativistic Monte Carlo code.

An expression for maximum accelerated particle energy Emax due to the firstorder shock-Fermi process is generalized to relativistic flows. Given the Bohm diffusion approximation and a mean ISM magnetic field of 3μG, then Emax ≈ 8 × 10β0Z(m⊙/n0) 1/3 eV for an uncollimated explosion expanding into a uniform medium with density n0. The initial flow speed of the explosion is β0c, and the total ejec...