Some properties of the dynamics of collapse in massive and massless relativistic theories of gravity

We investigate the dynamics of collapse in massive and massless relativistic theories of gravity for different equations of state for matter numerically and analytically. This allows clarifying the character of the collapse dynamics in the massive relativistic theory of gravity; in particular, we establish the graviton-mass dependence of the time of reaching the turning point (i.e., the point of transition from contraction to expansion). For the massless relativistic theory of gravity, we clarify the relation between the known general relativity solution for cold dust and the corresponding solution in the relativistic theory of gravity. We show that the harmonic time is singular, including the case of a smooth distribution of matter corresponding to a compact object with a strongly diffused boundary, which means that the Oppenheimer–Snyder solution cannot be fully embedded into the Minkowski space. We in addition investigate the effect of a nonzero pressure on the collapse dynamics.