$K$-Ricci-Bourguignon Almost Solitons

Year 2024, Volume: 17 Issue: 1, 63 - 71, 23.04.2024

U.c. De , Krishnendu De

https://doi.org/10.36890/iejg.1434598

Abstract

We in this current article introduce and characterize a $K$-Ricci-Bourguignon almost solitons in perfect fluid spacetimes and generalized Robertson-Walker spacetimes. First, we demonstrate that if a perfect fluid spacetime admits a $K$-Ricci-Bourguignon almost soliton, then the integral curves produced by the velocity vector field are geodesics and the acceleration vector vanishes. Then we establish that if perfect fluid spacetimes permit a gradient $K$-Ricci-Bourguignon soliton with Killing velocity vector field, then either state equation of the perfect fluid spacetime is presented by $p=\frac{3-n}{n-1}\sigma$ , or the gradient $K$-Ricci-Bourguignon soliton is shrinking or expanding under some condition. Moreover, we illustrate that the spacetime represents a perfect fluid spacetime and the divergence of the Weyl tensor vanishes if a generalized Robertson-Walker spacetime admits a $K$-Ricci-Bourguignon almost soliton.

Keywords

Perfect fluid spacetimes, GRW spacetimes, $K$ Ricci-Bourguignon solitons

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