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Previously we found that large amplitude $r$-modes could decay catastrophically due to nonlinear hydrodynamic effects. In this paper we found the particular coupling mechanism responsible for this catastrophic decay, and identified the fluid modes involved. We find that for a neutron star described by a polytropic equation of state with polytropic index $Gamma=2$, the coupling strength of the particular three-mode interaction causing the decay is strong enough that the usual picture of the $r$-mode instability with a flow pattern dominated by that of an $r$-mode can only be valid for the dimensionless $r$-mode amplitude less than $O(10^{-2})$.
We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are dest
In $f(R)$ gravity and Brans-Dicke theory with scalar potentials, we study the structure of neutron stars on a spherically symmetric and static background for two equations of state: SLy and FPS. In massless BD theory, the presence of a scalar couplin
We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near resonant inertial
In the context of f(R)=R + alpha R^2 gravity, we study the existence of neutron and quark stars with no intermediate approximations in the generalised system of Tolman-Oppenheimer-Volkov equations. Analysis shows that for positive alphas the scalar c
We derive the relativistic equations for stellar perturbations, including in a consistent way shear viscosity in the stress-energy tensor, and we numerically integrate our equations in the case of large viscosity. We consider the slow rotation approx