On 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. Firstly, for trapping to exist in an expansion-free dynamical star, the star must accelerate and radiate simultaneously. If either are zero, then the shear $Sigma$ must be zero through out the star, in which case the star is static ($\Theta=\Sigma=0$). Secondly, we prove that with nonzero acceleration and radiation expansion-free dynamical stars must be conformally flat.