$K$-Ricci-Bourguignon Almost Solitons

Authors : U C De, Krishnendu De

Pages : 63-71

Doi:10.36890/iejg.1434598

View : 85 | Download : 101

Publication Date : 2024-04-23

Article Type : Research Paper

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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