Original Conservation laws and invariant solutions of the wave equation on Bianchi I space-time: A comprehensive analysis

In accordance with Einstein's theory of general relativity, gravity is a phenomenon attributed to the curvature of spacetime. This notion has allowed physicists to investigate behaviour of physical processes, with respect to different curved spacetime, occurring in the presence of gravitation. One of the most basic of these processes is wave propagation whose various behaviours due to curvature effects have been investigated in the literature. This present study exhaustively explores the invariant solutions of the wave equation on Bianchi I space-time using Lie symmetry method. Under the isotropic Bianchi I universe, we showed how the aforementioned wave equation is connected to one of the most important equations encountered in the heat and mass transfer theory. Furthermore, we completely classify its conservation laws when the potentials are O(t(omega)) for any parameter omega.

Automated summary

This study extensively explores the invariant solutions of the wave equation on Bianchi I space-time using the Lie symmetry method, showcasing its connection to an important equation in heat and mass transfer theory under an isotropic Bianchi I universe. Furthermore, the conservation laws of the wave equation are completely classified when the potentials are O(t(omega)) for any parameter omega.