Dynamic conformal spherically symmetric solutions in an accelerated background

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.