Noether symmetries and conservation laws in some analytic spherically symmetric spacetimes of f(R, L m ) gravity

In general relativity, dark energy is usually illustrated by a cosmological constant(Λ), but f ( R , L m ) gravity provides a different approach to cosmic acceleration by modifying the gravitational theory. In the present paper, the non-static spherically symmetric spacetimes have been derived by taking into account f ( R , L m ) = f 1 ( R ) + H ( L m ) f 2 ( R ). Lie symmetry approach is operated to reduce the order of the partial differential equations corresponding to the field equations, which are further solved. Killing and Noether symmetries provides insights into the conservation laws. So, the obtained spacetimes have been investigated to obtain the Killing and Noether symmetries. The Lagrangian approach have been used to obtain the Noether symmetries. This study is well-structured, as it provides a justification for the well-established result that Noether symmetries encompass Killing symmetries [1]. Also the conserved quantities and commutators of Noether symmetries have been calculated.