Instability Analysis of Cylindrical Stellar Object in Brans-Dicke Gravity

This paper investigates instability ranges of a cylindrically symmetric collapsing stellar object in Brans-Dicke theory of gravity. For this purpose, we use perturbation approach in the modified field equations as well as dynamical equations and construct a collapse equation. The collapse equation with adiabatic index ($\mathrm{\Gamma }$) is used to explore the instability ranges of both isotropic as well as anisotropic fluid in Newtonian and post-Newtonian approximations. It turns out that the instability ranges depend on the dynamical variables of collapsing fluid. We conclude that the system always remains unstable for $0<\mathrm{\Gamma }<1$ while $\mathrm{\Gamma }>1$ provides instability only for the special case.