\noindent in this talk, i will discuss a novel class of nonlinear dispersive equations, which describe the dynamical evolution of self-gravitating relativistic matter. in fact, the analysis of these model equations will give a mathematical vindication of chandrasekhar's acclaimed physical theory of gravitational collapse. in particular, i will present results concerning the well-posedness of the initial-value problem, the singularity formation of solutions (blowup), as well as solitary wave solutions and their stability. time permitting, i will also discuss some recent and ongoing work. \\ \noindent this is partly joint work with j\"urg fr\""ohlich (eth z\""urich)