  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.
