A study of energy conditions in non-static spherically symmetric spacetimes via Noether symmetries

In this article, we have studied different energy conditions in non-static spherically symmetric spacetimes through Noether symmetries. The Lagrangian corresponding to the non-static spherically symmetric metric is used to obtain the set of determining equations of Noether symmetries. These equations are integrated to get a general solution in terms of some unknown functions of two variables, giving a list of integrability conditions. The ‘rifsimp’ command in Maple is used to classify the metric functions. Solving the integrability conditions for all possible cases, we obtain Noether algebras of dimension 4, 5, 6, 7, 8, 9 and 17. Some physical implications of the obtained metrics, including conservation laws and energy conditions, are also discussed for all the obtained metrics.