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Extending a previous work by the same authors, we investigate the existenceof expansion-free dynamical stars with non-zero spatial twist and rotation andshow that such stars cannot exist. Firstly, it is shown that a rotatingexpansion-free dynamical star with zero twist cannot exist. This is due to thefact that such stars cannot radiate and they are shear-free, in which case theenergy density $\rho$ is time independent. Secondly, we prove that anon-rotating expansion-free dynamical star with non-zero spatial twist alsocannot exist, as either the strong energy condition must be violated, i.e.$\rho+3p<0$, or the star must be shear-free in which case the star is static($\Theta=\Omega=\Sigma=0$). Finally, if we insist that the rotation and spatialtwist are simultaneously non-zero, then the star cannot be shear-free in whichcase we obtain a quadratic polynomial equation in $\phi$ and $\Sigma$ with noreal solutions. Therefore such stars cannot exist.

Non-existence of expansion-free dynamical stars with rotation and spatial twist