Complete classification of spherically symmetric static spacetimes via Noether symmetries

摘要

In this paper we give a complete classification of spherically symmetricstatic space-times by their Noether symmetries. The determining equations forNoether symmetries are obtained by using the usual Lagrangian of a generalspherically symmetric static spacetime which are integrated for each case. Inparticular we observe that spherically symmetric static spacetimes arecategorized into six distinct classes corresponding to Noether algebra ofdimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write downthe first integrals for each class of such spacetimes corresponding to theirNoether symmetries. Some new spherically symmetric static solutions have alsobeen obtained.