Some Novel Results on (alpha, beta)-Ricci-Yamabe Soliton and its Spacetime

TL;DR

This paper explores the properties of (alpha, beta)-Ricci-Yamabe solitons within Lorentzian para Sasakian spacetimes, examining various geometric conditions and providing a concrete example.

Contribution

It introduces new results on (alpha, beta)-Ricci-Yamabe solitons in Lorentzian para Sasakian manifolds, including specific cases and an explicit example.

Findings

Analysis of Ricci tensor conditions on (RYS)

Study of gradient (RYS) in LPS manifolds

Construction of a four-dimensional LPS manifold example

Abstract

This article aims to investigate the characteristics of (alpha, beta) Ricci Yamabe soliton (briefly (alpha, beta) (RYS)) and its spacetime. The inclusion of killing vector field and the Lorentzian metrics make the Ricci-Yamabe soliton richer and interesting. We study the cosmological and dust fluid model on (RYS) equipped with Lorentzian para Sasakian (LPS) spacetime. The cases of eta-parallel Ricci tensor and the Poisson structure have been studied on (RYS) equipped with (LPS) manifold. Gradient (RYS) equipped with (LPS) manifold also reveal. Finally, we establish an example of four-dimensional LP Sasakian manifold (LPS) that satisfy (alpha, beta) (RYS) and some results.