Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime with Torse-forming Vector Field

TL;DR

This paper explores the geometric properties of perfect fluid spacetimes with torse-forming vector fields and characterizes Ricci solitons within this context, including their expansion, steadiness, or shrinking behavior.

Contribution

It provides a detailed analysis of Ricci solitons in perfect fluid spacetimes with torse-forming vector fields, highlighting conditions for their different types.

Findings

Conditions for Ricci solitons to be expanding, steady, or shrinking.

Geometrical descriptions of perfect fluid spacetimes with torse-forming vector fields.

Characterization of Ricci solitons in this geometric setting.

Abstract

In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field \xi are discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field \xi are determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.