General Relativistic Space-Time with η1-Einstein Metrics

The present research paper consists of the study of an eta(1)-Einstein soliton in general relativistic space-time with a torse-forming potential vector field. Besides this, we try to evaluate the characterization of the metrics when the space-time with a semi-symmetric energy-momentum tensor admits an eta(1)-Einstein soliton, whose potential vector field is torse-forming. In adition, certain curvature conditions on the space-time that admit an eta(1)-Einstein soliton are explored and build up the importance of the Laplace equation on the space-time in terms of eta(1)-Einstein soliton. Lastly, we have given some physical accomplishment with the connection of dust fluid, dark fluid and radiation era in general relativistic space-time admitting an eta(1)-Einstein soliton.