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

Abstract

We compare the gravitational collapse of homogeneous perfect fluid with various equations of state in the framework of General Relativity and in [Formula: see text] gravity. We make our calculations using dimensionless time with characteristic timescale [Formula: see text], where [Formula: see text] 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 [Formula: see text] gravity, we have additional degree of freedom for initial conditions of collapse. For barotropic equation of state (EoS) [Formula: see text], the result depends from the value of parameter [Formula: see text]: for [Formula: see text] the collapse occurs slowly in comparison with General Relativity while for [Formula: see text], 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 [Formula: see text] (where [Formula: see text] and [Formula: see text] are the kinetic and potential energy of the field, respectively) and consider the corresponding Klein–Gordon equation for phantom scalar field.