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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 06
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219887822500815
  • Title of Journal : INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Keywords: Generalized Ricci solitons, torqued vector field, twisted product, perfect fluids, Robertson-Walker spacetime, Petrov types, EINSTEIN, CLASSIFICATION, MANIFOLDS

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.