Generalized Ricci—Bourguignon solitons on Lorentzian para-Sasakian manifolds and their applications in spacetimes

The principal aim of the present article is to characterize certain properties of Lorentzian para-Sasakian manifolds with generalized Ricci—Bourguignon solitons. We find a sufficient condition for a Lorentzian para-Sasakian manifold admitting generalized Ricci—Bourguignon solitons to be an $\eta$-Einstein manifold. We also construct a non-trivial example to verify the deduced results. Moreover, we analyze generalized Ricci—Bourguignon solitons in the perspective of $4$-dimensional Lorentzian para-Sasakian spacetimes.