General Relativistic Space-Time with <i>η</i>₁-Einstein Metrics

Abstract

The present research paper consists of the study of an η1-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 η1-Einstein soliton, whose potential vector field is torse-forming. In adition, certain curvature conditions on the space-time that admit an η1-Einstein soliton are explored and build up the importance of the Laplace equation on the space-time in terms of η1-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 η1-Einstein soliton.

Keywords

• general relativistic space-time
• torse-forming vector fields
• <i>η</i>₁-Einstein soliton
• Einstein’s field equation
• dust fluid
• dark fluid