  We consider dynamical spherically symmetric spacetimes, which are conformal
to the static spherically symmetric metrics, and find new solutions of Einstein
equations by symmetry considerations. Our study help us classify various
conformal Black Holes that are embedded within a dynamic background into the
one class of solutions with the same conformal symmetry. In addition,
Thermodynamics, mathematical and gravitational properties are addressed. These
solutions point to have a better resolution of the meaning of the Black Holes
in the dynamic background.
