Dynamical instability and expansion-free condition in $$f(R, T)$$ f ( R , T ) gravity

Abstract

A dynamical analysis of a spherically symmetric collapsing star surrounded by a locally anisotropic environment under an expansion-free condition is presented in f (R, T ) gravity, where R corresponds to the Ricci scalar and T stands for the trace of the energy momentum tensor. The modified field equations and evolution equations are reconstructed in the framework of f (R, T ) gravity. In order to acquire the collapse equation we implement the perturbation on all matter variables and dark source components comprising the viable f (R, T ) model. The instability range is described in the Newtonian and post-Newtonian approximation. It is observed that the unequal stresses and density profile define the instability range rather than the adiabatic index. However, the physical quantities are constrained to maintain positivity of the energy density and a stable stellar configuration. IntroductionThe astrophysics and astronomical theories are invigorated largely by the gravitational collapse and instability range explorations of self-gravitating objects. Celestial objects tend to collapse when they exhaust all their nuclear fuel, and gravity takes over as the inward governing force. The gravitating bodies undergoing collapse face contraction to a point, which results in high energy dissipation in the form of heat flux or radiation transport [1]. The end state of stellar collapse has been studied extensively, a continual evolution of a compact object might end up as a naked singularity or as a black hole depending upon the size of a collapsing star and also on the background that plays an important role in pressure-togravity imbalances [2][3][4]. a e-mail: ifra.noureen@gmail.com b e-mail: mzubairkk@gmail.com; drmzubair@ciitlahore.edu.pkThe gravitating objects are interesting only when they are stable against fluctuations; supermassive stars tend to be more unstable in comparison to the less massive stars [5]. The instability problem in a star's evolution is of fundamental importance; Chandrasekhar [6] presented the primary explorations on the dynamical instability of spherical stars. He identified the instability range of a star having mass M and radius r by a factor pertaining to the inequality ≥ 4 3 + n M r . The adiabatic index measures the compressibility of the fluid i.e., the variation of the pressure with a given change in the density. The analysis of expanding and collapsing regions in a gravitational collapse was presented by Sharif and Abbas [7].Herrera et al. [8][9][10][11] presented the dynamical analysis associated with isotropy, local anisotropy, shear, radiation, and dissipation with the help of ; it was established that minor alterations from an isotropic profile or a slight change in shearing effects bring about drastic changes in the range of instability. However, the instability range of stars with zero expansion does not depend on the stiffness of the fluid, but rather on other physical parameters [12][13][14], such as the mass distribution, the energy density profile, and the radial and tan...

Stellar equilibrium configurations of compact stars inf(R,T) theory of gravity

“…Conditions on the adiabatic index were constructed for Newtonian and post-Newtonian eras in order to address the instability problem. In [24], the authors have developed the instability range of the f (R, T ) theory for an anisotropic background constrained by zero expansions. The evolution of a spherical star by employing a perturbation scheme on the f (R, T ) field equations was explored in [25], while the dynamical analysis for gravitating sources carrying axial symmetry was discussed in [26].…”

Metric-Affine Myrzakulov Gravity Theories

“…In recent years, many investigations have been carried out to describe the present cosmic acceleration also in the setup of F(R, T ) gravity [57][58][59][60][61][62][63]. Moreover, several homogeneous isotropic and anisotropic cosmological models have been constructed in this context [64][65][66][67][68][69][70][71]. In particular, in [68] a Λ(t) cosmological model capable of explaining the recent astronomical observations of accelerating expansion of the universe with a decelerating phase of evolution in the past was obtained by a simple parametrization of the Hubble parameter in a flat FLRW spacetime in F(R, T ) gravity.…”

Role of Extended Gravity Theory in Matter Bounce Dynamics

“…In General Relativity (GR) and f (R, T) gravity, locally rotationally symmetric (LRS) Bianchi type-I viscous and non viscous cosmological models are investigated [61]. Energy conditions [62][63][64], perturbation analysis and stability analysis [65,66], cosmological solutions [67,68], dynamical instability [69] and astrophysical scenarios [70,71] have all been widely explored using the f (R, T) theory.…”