Gradient solitons on twisted product manifolds and their applications in general relativity

Gfiler S., Tastan H. M.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.19, sa.10, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 10
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s0219887822501547
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Twisted product, warped product, gradient Ricci soliton, gradient Yamabe soliton, generalized Robertson-Walker spacetime, standard static spacetime, ETA-RICCI SOLITONS, CURVATURE, GEOMETRY
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this paper, first, we find the necessary and sufficient condition for a Riemannian manifold to be the locally warped product. Then we investigate the existence of different types of gradient solitons, such as gradient (almost) Yamabe soliton, conformal soliton and gradient Ricci soliton on the twisted product manifolds. We also study the concircular flatness condition on a twisted product and examine the Einstein-type relations on its base and fiber manifold. Moreover, we introduce the notions of twisted generalized Robertson-Walker spacetime and twisted standard static spacetime. We get an ordinary differential equation (ODE) that determines the twisting function of the former and the exact form of the twisting function for the latter one.