Complete classification of spherically symmetric static space–times via Noether symmetries

We provide a complete classification of spherically symmetric static space–times by their Noether symmetries. We obtain the determining equations for the Noether symmetries using the usual Lagrangian of a general spherically symmetric static space–time and integrate them in each considered case. In particular, we find that spherically symmetric static space–times are categorized into six distinct classes corresponding to the Noether algebras of dimensions $5$, $6$, $7$, $9$, $11$, and $17$. Using Noether`s theorem, we also find the first integrals corresponding to each symmetry. Moreover, we obtain some new spherically symmetric static solutions.