New Results on the Perfect Fluid Lorentzian Para-Sasakian Spacetimes

Year 2025, Volume: 13 Issue: 1, 1 - 13, 30.04.2025

Sunıl Yadav , Ahmet Yıldız

https://izlik.org/JA72AW78FP

Abstract

In this article, we investigate $\mathcal{LP}$-Sasakian spacetimes attached with perfect fluid whose metrics are (CERY)$_{4}$-soliton admitting $% \mathcal{Z}$-tensor. Also we discuss the application of such soliton to cosmology and general relativity. Besides this, we deduce a modified Poisson equation and modified Liouville equation from the (CERY)$_{4}$-soliton on $% \mathcal{LP}$-Sasakian spacetimes . In addition, we light up the harmonic aspect of such soliton on perfect fluid $\mathcal{LP}$-Sasakian spacetimes. Moreover, we conclude a necessary and sufficient condition for a $1$-form $% \eta ^{\sharp }$, which is the $g^{\star }$-dual of the vector field $\xi $ on such a spacetime to be a solution of the Schr\"{o}dinger-Ricci equation. In conclusion, we present an instance of a $4$-dimensional $\mathcal{LP}$% -Sasakian spacetime with the (CERY)$_{4}$-soliton equipped with $\mathcal{Z}$% -tensor.

Keywords

LP-Sasakian manifold , Z-tensor , conformal eta-Ricci Yamabe soliton , Schrodinger-Ricci equation , Modified Possion equation

Ethical Statement

There are no any Ethical statement

Supporting Institution

NA

Project Number

NA

Thanks

NA

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