Kahlerian Spacetime and η-Einstein Solitons

Abstract

This paper is dedicated to the study of the geometric composition of a K¨ahlerian spacetime with a η-Einstein soliton. Here, we have delineated the nature such soliton on a K¨ahlerian spacetime to be expanding, steady, or shrinking under various physical conditions depend on isotropic pressure, cosmological constant, energy density, and gravitational constant relations. We have also discussed η-Ricci soliton on some special types of perfect fluid spacetime such as dust fluid, viscous fluid, dark fluid and radiation era.

Keywords: K¨ahler spacetime; Quasi-conformal curvature tensor; Weakly symmetric; Weakly Ricci symmetric; Perfect fluid; Dust fluid and viscous fluid.

2010 Mathematics Subject Classification. 53C15; 53C50; 53B15; 53B20