Static perfect fluid spacetime on Riemannian manifolds admitting concurrent-recurrent vector field with Bach tensor-Reference-Cited by-同舟云学术

Static perfect fluid spacetime on Riemannian manifolds admitting concurrent-recurrent vector field with Bach tensor

Published:2024-09-03 Issue: Volume: Page:
ISSN:1425-6908
Container-title:Journal of Applied Analysis
language:en
Short-container-title:

Author:

Praveena M. M.¹^ORCID,Kumara H. Aruna²,Arjun C. M.³,Siddesha M. S.⁴

Affiliation:

1. Department of Mathematics , 154018 M. S. Ramaiah Institute of Technology (affiliated to VTU), Bangalore - 560054, Karnataka , India

2. Department of Mathematics , BMS Institute of Technology and Management , Yelahanka Campus-560064 , Bangalore , Karnataka , India

3. Department of Mathematics , M. S. Ramaiah Institute of Technology (affiliated to VTU), Bangalore - 560054, Karnataka , India

4. Department of Mathematics , Jain Deemed-to-be-University , Global Campus-562112 , Bangalore , Karnataka , India

Abstract

Abstract In this paper, we first consider the 𝕊 ⁢ ℙ ⁢ 𝔽

{\mathbb{SPF}}

equation on a Riemannian CRVF-manifold M and show that either M is Einstein or the potential function is pointwise collinear with ζ on an open set U of M. Next, we show that if a Riemannian CRVF-manifold M is the spatial factor of a 𝕊 ⁢ ℙ ⁢ 𝔽

{\mathbb{SPF}}

with a Batch tensor then it is a Batch flat space-time manifold.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/jaa-2024-0018/pdf

Reference20 articles.

1. L. Ambrozio, On static three-manifolds with positive scalar curvature, J. Differential Geom. 107 (2017), no. 1, 1–45.

2. R. Bach, Zur Weylschen Relativitätstheorie und der Weylschen Erweiterung des Krümmungstensorbegriffs, Math. Z. 9 (1921), no. 1–2, 110–135.

3. F. Carolina and N. Jose, A Riemannian manifolds dual to static spacetimes, Gen. Rel. Grav. 52 (2020), Paper No. 84.

4. Q. Chen and C. He, On Bach flat warped product Einstein manifolds, Pacific J. Math. 265 (2013), no. 2, 313–326.

5. Y. Cho, Y. Degura and K. Shiraishi, Extremely charged static perfect fluid distributions with dilaton in curved spacetimes, Phys. Rev. 62 (2000), Article ID 084038.