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Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity

Uday Chand De, Krishnendu De

Abstract

In this article we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes. At first, we produce an example to justify the existence of such a spacetime. Then, it is provided that a pseudo generalized Ricci-recurrent generalized Robertson-Walker spacetime represents a perfect fluid spacetime and a pseudo generalized Ricci-recurrent perfect fluid spacetime represents either a dark energy epoch of the Universe or, the velocity vector field is parallel, conservative, acceleration-free, vorticity-free, and shear-free and becomes a static spacetime. Lastly, we study the impact of this spacetime under $f(\mathcal{R})$ gravity scenario and deduce several energy conditions.

Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity

Abstract

In this article we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes. At first, we produce an example to justify the existence of such a spacetime. Then, it is provided that a pseudo generalized Ricci-recurrent generalized Robertson-Walker spacetime represents a perfect fluid spacetime and a pseudo generalized Ricci-recurrent perfect fluid spacetime represents either a dark energy epoch of the Universe or, the velocity vector field is parallel, conservative, acceleration-free, vorticity-free, and shear-free and becomes a static spacetime. Lastly, we study the impact of this spacetime under gravity scenario and deduce several energy conditions.

Paper Structure

This paper contains 13 sections, 9 theorems, 113 equations, 1 table.

Table of Contents

  1. Introduction
  2. Example of a $P\left(GR_{4}\right)$ spacetime
  3. $P\left(GR_{4}\right)$ GRW spacetimes
  4. $P\left(GR_{4}\right)$ $\mathrm{perfect\, fluid\, spacetimes}$
  5. $P\left(GR_{4}\right)$ GRW spacetime in $f(\mathcal{R})$ gravity
  6. Energy Conditions
  7. Energy Conditions
  8. Discussion
  9. Declarations
  10. Funding
  11. Code availability
  12. Availability of data
  13. Conflicts of interest

Key Result

Theorem 1

A $P\left(GR_{4}\right)$$\mathrm{GRW}$ spacetime represents a $\mathrm{PFS}$.

Theorems & Definitions (11)

  • Theorem 1
  • Corollary 1
  • Definition 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Corollary 2
  • Remark 1
  • ...and 1 more