New Results on the Perfect Fluid Lorentzian Para-Sasakian Spacetimes

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

Supporting Institution

NA

Project Number

NA

Ethical Statement

There are no any Ethical statement

Thanks

NA

References

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