Gravitational Collapse in General Relativity and in $R^2$-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 $R^2$ gravity. We make our calculations using dimensionless time with characteristic timescale $t_g\sim (G\rho {)}^{-1/2}$ 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 $p=w\rho$ 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 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.

18 pp., accepted in IJGMMP

References in corpus (5)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Time-dependent matter instability and star singularity in $F(R)$ gravity
• Gravitational Perfect Fluid Collapse in f(R) Gravity

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• Is gravitational collapse possible in $f(R)$ gravity?
• Wormhole modeling in $R^2$ gravity with linear trace term