Stable Self-similar Blow up Dynamics for the Three Dimensional Relativistic Gravitational Vlasov-poisson System

and σN is the area of the unit sphere in R (σ3 = 4π and σ4 = 2π). This nonlinear transport equation describes in dimension N = 3 the mechanical state of a stellar system subject to its own gravity (see for instance [3, 14]). Classical calculations show that this model should be correct only for low velocities, and if high velocities occur, special relativistic corrections should be introduced; see Van Kampen and Felderhof [44], Glassey and Schaeffer [18] and references therein. A more accurate model is then provided by the three dimensional relativistic gravitational VlasovPoisson system: (1.3)