Newtonian and post Newtonian expansionfree fluid evolution in f(R) gravity

Abstract

We consider a collapsing sphere and discuss its evolution under the vanishing expansion scalar in the framework of f (R) gravity. The fluid is assumed to be locally anisotropic which evolves adiabatically. To study the dynamics of the collapsing fluid, Newtonian and post Newtonian regimes are taken into account. The field equations are investigated for a well-known f (R) model of the form R + δR 2 admitting Schwarzschild solution. The perturbation scheme is used on the dynamical equations to explore the instability conditions of expansionfree fluid evolution. We conclude that instability conditions depend upon pressure anisotropy, energy density and some constraints arising from this theory.

Dissipative spherical collapse of charged anisotropic fluid in $$f(R)$$ f ( R ) gravity

“…For the interior spacetime, the components on the right hand side of the field equations (2.5) are given as follows, whereas the components of the Einstein tensor are present in [12]:…”

“…The impressions of radiation, anisotropy, and shearing viscosity at Newtonian and post-Newtonian eras are inquired in [5][6][7][8]. Various prospects of the collapse phenomenon to account for dark source have been worked out in the recent past [9][10][11][12][13][14]. Due to a high dissipation, matter produces a large amount of charge in the collapse phenomenon and so one is well motivated to investigate the effects of the electromagnetic field on the gravitational collapse [15].…”

Effects of CDTT model on the dynamical instability of cylindrically symmetric collapsing stars

“…(3.17) and then integrating resulting equation with respect to "t" , we 19) where φ 3 (r) is given in Appendix. Considering the second law of thermodynamics, we can express a relationship betweenρ andp r as the ratio of specific heat by assuming an equation of state of Harrison-Wheeler type as follows [48,49]…”

Dynamical analysis of cylindrically symmetric anisotropic sources in f(R, T) gravity

“…Meanwhile, Gosh and Maharaj [20] established exact solutions of a null dust non-static cluster of particles in f (R) gravity, constrained by constant curvature describing an anti de Sitter background. Some highly important prospects of celestial collapse for f (R) theory are worked out in [21][22][23][24]. Sharif and Bhatti [25] discussed the instability conditions for cylindrically symmetric self-gravitating objects surrounded by a charged expansionfree anisotropic environment.…”