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The continuously decreasing curvature of spacetime has been proposed to be due to the phenomenon like Hawking radiation, the collapse of black holes and neutron stars. It has been found that during these phenomena, energy of source (black hole and neutron stars) decreases. In this paper, we explore this loss in energy of the source by introducing a time conformal factor in the corresponding spacetime in order to get a nonstatic metric without violating its symmetry structure. This technique gives us information about the loss of momentum and energy of the source. We also consider some novel nonstatic classes of the plane-symmetric spacetime containing 10 Noether symmetries and 7 isometries.

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