Gravitational collapse in General Relativity and in R2-gravity: A comparative study

We compare the gravitational collapse of homogeneous perfect fluid with various equations of state in the framework of General Relativity and in R-2 gravity. We make our calculations using dimensionless time with characteristic timescale t(g) similar to (G(rho))(-1/2), where rho is a density of collapsing matter. The cases of matter, radiation and stiff matter are considered. We also account the possible existence of vacuum energy and its influence on gravitational collapse. In a case of R-2 gravity, we have additional degree of freedom for initial conditions of collapse. For barotropic equation of state (EoS) p = w rho, the result depends from the value of parameter w: for w > 1/3 the collapse occurs slowly in comparison with General Relativity while for w < 1/3, we have the opposite situation. Vacuum energy as expected slows down the rate of collapse and for some critical density gravitational contraction may change to expansion. It is interesting to note that for General Relativity such expansion is impossible. We also consider the collapse in the presence of so-called phantom energy. For description of phantom energy, we use Lagrangian in the form -X - V (where X and V are the kinetic and potential energy of the field, respectively) and consider the corresponding Klein-Gordon equation for phantom scalar field.