Instability of meridional axial system in f(R) gravity

We analyze the dynamical instability of a non-static reflection axial stellar structure by taking into account the generalized Euler equation in metric f(R) gravity. Such an equation is obtained by contracting the Bianchi identities of the usual anisotropic and effective stress-energy tensors, which after using a radial perturbation technique gives a modified collapse equation. In the realm of the $$R+\epsilon R^n$$ gravity model, we investigate instability constraints at Newtonian and post-Newtonian approximations. We find that the instability of a meridional axial self-gravitating system depends upon the static profile of the structure coefficients, while f(R) extra curvature terms induce the stability of the evolving celestial body.

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