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Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons

Krishnendu De, Mohammad Nazrul Islam Khan, Uday Chand De

Abstract

In this article, we examine gradient type Ricci solitons and $(m,τ)$-quasi Einstein solitons in generalized Robertson-Walker ($GRW$) spacetimes. Besides, we demonstrate that in this scenario the $GRW$ spacetime presents the Robertson-Walker ($RW$) spacetime and the perfect fluid ($PF$) spacetime presents the phantom era. Consequently, we show that if a $GRW$ spacetime permits a gradient $τ$- Einstein solitons, then it also represents a $PF$ spacetime under certain condition.

Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons

Abstract

In this article, we examine gradient type Ricci solitons and -quasi Einstein solitons in generalized Robertson-Walker () spacetimes. Besides, we demonstrate that in this scenario the spacetime presents the Robertson-Walker () spacetime and the perfect fluid () spacetime presents the phantom era. Consequently, we show that if a spacetime permits a gradient - Einstein solitons, then it also represents a spacetime under certain condition.
Paper Structure (4 sections, 10 theorems, 74 equations)

This paper contains 4 sections, 10 theorems, 74 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of the prime Theorems
  4. Discussion

Key Result

Theorem 1.1

(survey) The Lorentzian manifold $\mathcal{M}^{n}$ ($n \ge 3$) is a $GRW$ spacetime iff the spacetime permits a unit torse-forming time-like vector field : $\nabla_{j}u_{k}=\psi (g_{ik}+u_{k}u_{i})$, it is also an eigenvector of the Ricci tensor.

Theorems & Definitions (13)

  • Definition 1.1
  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Corollary 3.1
  • Remark 1
  • Corollary 3.2
  • ...and 3 more