An Eternal gravitational collapse in f(R) theory of gravity and their astrophysical implications

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The present investigation explores a novel facet of gravitational collapse, surpassing conventional notions of black holes and naked singularities. In this work, we explore a new aspects on the final fate of Gravitational Collapse of a stellar system within the framework of f(R) gravity and find the continued homogeneous gravitational collapse: an eternal collapsing phenomenon. The exact solutions of field equations have been obtained in an independent way by the parametrization of the expansion scalar (Θ) governed by the interior spherically symmetric FLRW metric. We impose the Darmois junction condition required for the smooth matching of the interior region to the Schwarzschild exterior metric across the boundary hypersurface of the star. The junction conditions demand that the pressure is non-vanishing at the boundary and is proportional to the non-linear terms of f(R) gravity, and the mass function m(t,r) is equal to Schwarzschild mass M. The eight massive stars, namely Westerhout49−2,BAT99−98,R136a1,R136a2,WR24,Pismis24−1, λ−Cephei, and β−CanisMajoris with their known astrophysical data (masses and radii) are used to estimate the numerical values of the model parameters which allows us to study the solutions numerically and graphically. Here we have discussed two f(R) gravity models describing the collapse phenomenon. The singularity analysis of models is discussed via the apparent horizon and we have shown that stars tend to collapse for an infinite co-moving time in order to attain the singularity (an eternal collapsing phenomenon). We have also shown that our models satisfy the energy conditions and stability requirements for stellar systems.