Instability of Meridional Axial System in f(R) Gravity

Evolution of Axially Symmetric Anisotropic Sources in $f(R,T)$ 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 $Γ$ that defines…

Axial instability of rotating relativistic stars

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{imϕ}$ for all values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low $m$-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of $m$. The timescale for the axial instability appears, for small angular velocity $Ω$, …

Axially Symmetric Shear-free Fluids in $f(R,T)$ Gravity

In this work we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in $f(R,T)$ theory. Restricted axial symmetry ignoring rotation and reflection enteries is taken into account for establishment of instability range. Implementation of linear perturbation on constitutive modified dynamical equations yield evolution equation. This equation associates adiabatic index $Γ$ with material and dark source components defining stable and unstable regions in Newtonian (N) and post-Newtonian (pN) approximations.

利用谱方法对大规模静态幻影虫洞的不稳定性分析

Instability Analysis of Massive Static Phantom Wormholes via the Spectral Method

本文利用谱方法研究大规模静态幻影虫洞的标量与轴向准正则模式，发现新的纯虚模式并揭示其不稳定性条件，为幻影虫洞稳定性提供新见解。

Stability of a Class of Non-Static Axial Self-Gravitating Systems in $f(R)$ Gravity

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider $f(R)=R+εR^2$ model and assume hydrostatic equilibrium of the axial self-gravitating 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 high…

Approximate equation relevant to axial oscillations on slowly rotating relativistic stars

Axial oscillations relevant to the r-mode instability are studied with slow rotation formalism in general relativity. The approximate equation governing the oscillations is derived with second-order rotational corrections. The equation contains an effective 'viscosity-like' term, which originates from coupling to the polar g-mode displacements. The term plays a crucial role on the resonance point, where the disturbance on the rotating stars satisfies a certain condition at the lowest order equation. The effect is significant for newly born hot neutron stars, which are expected to be subject to…