Dark energy models based on f (R) theory have been extensively studied in literature to realize the late time acceleration. In this paper, we have chosen a viable f (R) model and discussed its effects on the dynamical instability of expansionfree fluid evolution generating a central vacuum cavity. For this purpose, contracted Bianchi identities are obtained for both the usual matter as well as dark source. The term dark source is named to the higher order curvature corrections arising from f (R) gravity. The perturbation scheme is applied and different terms belonging to Newtonian and post Newtonian regimes are identified. It is found that instability range of expansionfree fluid on external boundary as well as on internal vacuum cavity is independent of adiabatic index Γ but depends upon the density profile, pressure anisotropy and f (R) model.

Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in f(R) theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show that this is in general not possible and, in particular, that the traceless condition cannot be imposed due to the fact that we no longer have a Minkowski background metric. Our findings are in agreement with the results found using the Newman-Penrose formalism and thus clarify the inconsistencies found so far in the literature. Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in f (R) theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show that this is in general not possible and, in particular, that the traceless condition cannot be imposed due to the fact that we no longer have a Minkowski background metric. Our findings are in agreement with the results found using the Newman-Penrose formalism, and thus clarify the inconsistencies found so far in the literature.

This manuscript is devoted to the study of the combined effect of a viable f (R) = R + α R n model and the electromagnetic field on the instability range of gravitational collapse. We assume the presence of a charged anisotropic fluid that dissipates energy via heat flow and discuss how the electromagnetic field, density inhomogeneity, shear, and phase transition of astrophysical bodies can be incorporated by a locally anisotropic background. The dynamical equations help to investigate the evolution of self-gravitating objects and lead to the conclusion that the adiabatic index depends upon the electromagnetic background, mass, and radius of the spherical objects.

In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric f (R) gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f (R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude that the constant scalar curvature term f (R 0 ) acts as a source of repulsive force and thus slows down the collapse of matter. The comparison with the corresponding results available in general relativity indicates that f (R 0 ) plays the role of the cosmological constant.