Geometric study of Ricci solitons in perfect fluid spacetimes with Lorentzian concircular structure manifolds

Abstract

In this article, we examine the interaction between Ricci solitons and the properties of the geometric structure in a perfect fluid spacetimes that admits a Lorentzian Concircular structure manifold with a Concircular curvature tensor. We investigate the conditions under which a Ricci soliton exists within such a framework and analyze its implications on the curvature properties of the spacetime. The study focuses on the influence of the soliton potential on the energy-momentum tensor of the perfect fluid and examines the interplay between the Ricci curvature and the Concircular structure. Further, we establish key geometric conditions that characterize the nature of the Ricci soliton in this setting and derive significant constraints on the manifolds topology. Our findings contribute to the broader understanding of the role of Ricci solitons in relativistic fluids and their impact on spacetime geometry.