Dynamical Instability and Expansion-free Condition in f(R,T)f(R,T) Gravity

Dynamical analysis of spherically symmetric collapsing star surrounding in locally anisotropic environment with expansion-free condition is presented in $f(R,T)$ gravity, where $R$ corresponds to Ricci scalar and $T$ stands for the trace of energy momentum tensor. The modified field equations and evolution equations are reconstructed in the framework of $f(R,T)$ gravty. 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 Newtonian and post-Newtonian eras by constraining the adiabatic index $\Gamma$ to maintain viability of considered model and stable stellar configuration.Comment: 22 page

Evolution of Axially Symmetric Anisotropic Sources in f(R,T)f(R,T) Gravity

We discuss the dynamical analysis in $f(R,T)$ gravity (where $R$ is Ricci scalar and $T$ is trace of energy momentum tensor) for gravitating sources carrying axial symmetry. The self gravitating system is taken to be anisotropic and line element describes axially symmetric geometry avoiding rotation about symmetry axis and meridional motions (zero vorticity case). The modified field equations for axial symmetry in $f(R,T)$ theory are formulated, together with the dynamical equations. Linearly perturbed dynamical equations lead to the evolution equation carrying adiabatic index $\Gamma$ that defines impact of non-minimal matter to geometry coupling on range of instability for Newtonian (N) and post-Newtonian (pN) approximations.Comment: 19 page

Dynamical Analysis of Cylindrically Symmetric Anisotropic Sources in f(R,T)f(R,T) Gravity

In this paper, we have analyzed the stability of cylindrically symmetric collapsing object filled with locally anisotropic fluid in $f(R,T)$ theory, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor of matter. Modified field equations and dynamical equations are constructed in $f(R,T)$ gravity. Evolution or collapse equation is derived from dynamical equations by performing linear perturbation on them. Instability range is explored in both Newtonian and post-Newtonian regimes with the help of adiabetic index, which defines the impact of physical parameters on the instability range. Some conditions are imposed on physical quantities to secure the stability of the gravitating sources.Comment: 11 page

Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms

In this paper, we prove the existence and uniqueness of the continuous Green function G for the elliptic operator L = div(A(x)∇x)+B(x)·∇x with singular drift term B on a C1,1 bounded domain D in Rn, n ≥ 3, and its comparability to the Green function G0 of L0 = div(A(x)∇x). Basing on this result we establish the equivalence of the L-harmonic measure and the surface measure on ∂D. These results extend some first ones proved for elliptic operators with less singular drift terms

Shearfree Condition and dynamical Instability in f(R,T)f(R,T) gravity

The implications of shearfree condition on instability range of anisotropic fluid in $f(R,T)$ are studied in this manuscript. A viable $f(R, T)$ model is chosen to arrive at stability criterion, where $R$ is Ricci scalar and $T$ is the trace of energy momentum tensor. The evolution of spherical star is explored by employing perturbation scheme on modified field equations and contracted Bianchi identities in $f(R, T)$. The effect of imposed shearfree condition on collapse equation and adiabatic index $\Gamma$ is studied in Newtonian and post-Newtonian regimes.Comment: 16 page