Torqued vector fields on generalized Ricci solitons and Lorentzian twisted products


Guler S., Altay Demirbağ S.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.19, no.06, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 06
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219887822500815
  • Journal Name: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Generalized Ricci solitons, torqued vector field, twisted product, perfect fluids, Robertson-Walker spacetime, Petrov types, EINSTEIN, CLASSIFICATION, MANIFOLDS
  • Istanbul Technical University Affiliated: Yes

Abstract

In this study, some relations between the generalized Ricci solitons with generalized quasi-Einstein manifolds and twisted products are established. Then, an explicit example of generalized quasi-Einstein spacetime endowed with the spatially homogeneous and anisotropic Bianchi type-V metric is constructed. Also, we get certain identities about the Riemannian and the Ricci tensors on a Lorentzian twisted product (M = I x(f) F,g) admitting a timelike torqued vector field. We proved that such spacetime admitting a timelike torqued vector field having a closed torqued form is a generalized Robertson- Walker spacetime. Therefore, from Mantica and Molinari's classifications, this spacetime becomes a model of perfect fluids. As a physical application, it is shown that the magnetic parts of the Weyl tensor of such spacetime vanish and so its possible Petrov types are I , D or O.