On the symmetry and conservation law classification of the de Sitter-Schwarzschild metric and the corresponding wave and Klein-Gordon equations

The main purpose of this work is to focus on a discussion of Lie symmetries admitted by de Sitter-Schwarzschild spacetime metric, and the corresponding wave or Klein-Gordon equations constructed in the de Sitter-Schwarzschild geometry. The obtained symmetries are classified and the variational (Noether) conservation laws associated with these symmetries via the natural Lagrangians are obtained. In the case of the metric, we obtain additional variational ones when compared with the Killing vectors leading to additional conservation laws and for the wave and Klein-Gordon equations, the variational symmetries involve less tedious calculations as far as invariance studies are concerned.