Properties of expansion-free dynamical stars

We study the geometrical and dynamical features of expansion-free dynamical stars in general relativity. Such stars can exist only if particular physical and geometric conditions are satisfied. First, for trapping to exist in an expansion-free dynamical star, the star must accelerate and radiate simultaneously. If either is zero, then the shear ($\mathrm{\Sigma }$) must be zero throughout the star, in which case the star is static ($\mathrm{\Theta }=\mathrm{\Sigma }=0$). Second, we prove that with nonzero acceleration and radiation expansion-free dynamical stars must be conformally flat.