Stability of a class of non-static axial self-gravitating systems in f(R) gravity

Abstract

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider f (R) = R + ǫR 2 model and assume hydrostatic equilibrium of the axial selfgravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, Γ 1 , that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the f (R) model affect the instability ranges.

Structure scalars in dissipative axial system in f(R) gravity

“…By combining transport equation with generalized Euler equation, it turns out that the dissipative flux along with extra curvature f (R) terms tend to lessen the system inertial mass density. It is interesting to mention here that all our results reduce to GR [27] under α → 0 limit while the constraint G = 0 describes the restricted non-static axial system in f (R) gravity, which supports the analysis given in [20,21].…”

“…Equation (26) exhibits that there is only one independent nonvanishing component of the vorticity tensor, i.e., 12 . We would like to mention here that for = 0, we have zero non-diagonal metric coefficient, i.e., G = 0 whose dynamics has already been discussed both in GR [19] as well as f (R) gravity [20,21].…”

“…Herrera et al [18] studied static axially symmetric source with an imperfect anisotropic fluid distribution and obtained some analytical models with the help of scalar functions. Sharif and his collaborators [19,20] investigated axial collapse by neglecting the meridional and rotational metric properties with anisotropic matter configuration in GR as well as f (R) gravity and found that anisotropy tends to increase the collapse rate. Recently, we have explored expansion-free geodesic axial system in f (R) gravity [21] as well as in GR [22] coupled with anisotropic dissipative fluid configuration and concluded that the system preserves and deviates from its axial symmetry even in dissipation-less background respectively.…”

Role of tilted congruence and f(R) gravity on regular compact objects

“…(44). Therefore, the regular energy density can be achieved by the system if the system makes null value to the following parameter, Φ…”

Dynamics of magnetized string cosmological model in f(R,T) gravity theory

“…The f (R) gravity theory provides a very natural unification of early time inflation and late time accelerated expansion of the universe. Sharif and Yousaf (2014a) have analyzed the stability region of a non static restricted class of axially symmetric space-time with anisotropic matter distribution in f (R) gravity theory by taking f (R) = R + R 2 . Sharif and Yousaf (2014b) further analyzed various factors producing inhomogeneity in the energy density of the spherical self-gravitating celestial body in f (R) gravity and obtained evolution equations using a viable inflationary f (R) model.…”