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We explore the dynamics of collapsing stellar filament in the presence of exotic material like dark matter. We use Palatini  f ( R ) theory to include exotic substance in the collapsing process. We derive a collapse equation by applying Darmois junction conditions on collapsing surface boundary    $$\Sigma $$   Σ    . It is found that the radial pressure related to baryonic matter remains non-zero at    $$\Sigma $$   Σ    . We then discuss the stability criteria of the collapsing process in the framework of three parameteric model,    $$f(R)=R+\lambda R_{c}[ 1-(1+\frac{R^{2}}{R^{2}_{c}})^{-n}]$$    f   (  R  )   =  R  +  λ   R  c    [  1  -    (  1  +    R  2    R  c  2    )    -  n    ]. It is concluded that the stability of collapsing filament depends upon a directly proportional relation of gravitational effects of exotic terms with the radial pressure of seen matter. Stability criteria of family of polytropic filamentary structures are also discussed. For all stable polytropic filaments, it is found that the density of seen material is exponentially related to the exotic forces. Finally, we explore theoretical relation between gravitational waves and dark terms. It is theoretically predicted that the presence of exotic material can affect the propagation of gravitational waves.

Collapsing stellar filament and exotic matter in Palatini f(R) gravity