On generalized quasi Einstein standard static spacetimes

Sinem Güler; Sezgin Altay Demirbağ

doi:10.1016/j.geomphys.2021.104366

On generalized quasi Einstein standard static spacetimes

Sinem Güler^*, Sezgin Altay Demirbağ

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Sabahattin Zaim University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, (m,ρ)-quasi Einstein manifolds, and gradient Ricci solitons. Then, we obtain some necessary and sufficient conditions about the existence of certain vector fields on the standard static spacetime. We also characterize the m-quasi Einstein standard static spacetimes admitting concurrent or parallel vector fields and get several physical properties of such spacetimes. At last, we construct non-trivial examples of m-quasi Einstein spacetimes verifying our results.

Original language	English
Article number	104366
Journal	Journal of Geometry and Physics
Volume	170
DOIs	https://doi.org/10.1016/j.geomphys.2021.104366
Publication status	Published - Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Funding

This work is supported by the Research Fund of the Istanbul Technical University (GAP project reference TGA-2018-41211 ). The authors would like to thank the referee for reviewing the paper carefully and her or his valuable comments which provided insights to improve the quality of the results.

Funders	Funder number
Istanbul Teknik Üniversitesi	TGA-2018-41211

Keywords

Bakry-Emery Ricci tensor
Gradient Ricci soliton
m-generalized quasi Einstein manifold
m-quasi Einstein manifold
Standard static spacetime

Access to Document

10.1016/j.geomphys.2021.104366

Cite this

@article{833c61f134764575a70cb774e594ed96,

title = "On generalized quasi Einstein standard static spacetimes",

abstract = "In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, (m,ρ)-quasi Einstein manifolds, and gradient Ricci solitons. Then, we obtain some necessary and sufficient conditions about the existence of certain vector fields on the standard static spacetime. We also characterize the m-quasi Einstein standard static spacetimes admitting concurrent or parallel vector fields and get several physical properties of such spacetimes. At last, we construct non-trivial examples of m-quasi Einstein spacetimes verifying our results.",

keywords = "Bakry-Emery Ricci tensor, Gradient Ricci soliton, m-generalized quasi Einstein manifold, m-quasi Einstein manifold, Standard static spacetime",

author = "Sinem G{\"u}ler and {Altay Demirbağ}, Sezgin",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = dec,

doi = "10.1016/j.geomphys.2021.104366",

language = "English",

volume = "170",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - On generalized quasi Einstein standard static spacetimes

AU - Güler, Sinem

AU - Altay Demirbağ, Sezgin

PY - 2021/12

Y1 - 2021/12

N2 - In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, (m,ρ)-quasi Einstein manifolds, and gradient Ricci solitons. Then, we obtain some necessary and sufficient conditions about the existence of certain vector fields on the standard static spacetime. We also characterize the m-quasi Einstein standard static spacetimes admitting concurrent or parallel vector fields and get several physical properties of such spacetimes. At last, we construct non-trivial examples of m-quasi Einstein spacetimes verifying our results.

AB - In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, (m,ρ)-quasi Einstein manifolds, and gradient Ricci solitons. Then, we obtain some necessary and sufficient conditions about the existence of certain vector fields on the standard static spacetime. We also characterize the m-quasi Einstein standard static spacetimes admitting concurrent or parallel vector fields and get several physical properties of such spacetimes. At last, we construct non-trivial examples of m-quasi Einstein spacetimes verifying our results.

KW - Bakry-Emery Ricci tensor

KW - Gradient Ricci soliton

KW - m-generalized quasi Einstein manifold

KW - m-quasi Einstein manifold

KW - Standard static spacetime

UR - http://www.scopus.com/inward/record.url?scp=85114664940&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2021.104366

DO - 10.1016/j.geomphys.2021.104366

M3 - Article

AN - SCOPUS:85114664940

SN - 0393-0440

VL - 170

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

M1 - 104366

ER -

On generalized quasi Einstein standard static spacetimes

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this