A Study of Conformally Flat Quasi-Einstein Spacetimes with Applications in General Relativity

Venkatesha, V.; Kumara, A. Naveena

doi:10.46793/kgjmat2103.477v

Cited by 1 publication

(1 citation statement)

References 19 publications

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“…A. Shaikh, D. Y. Yoon and S. K. Hui have studied about the properties and the application of quasi-Einstein spacetime. Many more works have been done in the spacetime of general relativity [3], [19], [20], [21], [34] [46], [37], [47], [48], [49], [50], [51].…”

Section: Preliminariesmentioning

confidence: 99%

A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime

Chattopadhyay¹,

Bhattacharyya²,

Debnath³

2021

Preprint

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In the present paper we discuss about a set of geometric properties and physical applications of a mixed quasi-Einstein spacetime[M (QE) 4 ], which is a special type of nearly quasi-Einstein spacetime[N (QE) 4 ]. Firstly we consider a nearly quasi-Einstein manifold[N (QE) n ] along with a mixed quasi-Einstein manifold[M (QE) n ] and study some geometric conditions with respect to different curvature tensors on them. Then we consider a mixed quasi-Einstein spacetime and study W 2 -Ricci pseudosymmetry and projective Ricci pseudosymmetry on it. Then we study the conditions H • S = 0 and C • S = 0 in an M (QE) 4 spacetime, where H, C are the conharmonical curvature tensor and semiconformal curvature tensor respectively. Next we consider a semiconformally flat Ricci pseudosymmetric M (QE) 4 spacetime and find the nature of that spacetime. In the next section we study about some applications of a perfect fluid M (QE) 4 spacetime in the general theory of relativity. Followed by we discuss about the Ricci soliton structure in a semiconformally flat M (QE) 4 spacetime satisfying Einstein field equation without cosmological constant. Finally we give a nontrivial example of a M (QE) 4 spacetime to establish the existence of it.

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Section: Preliminariesmentioning

confidence: 99%

A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime

Chattopadhyay¹,

Bhattacharyya²,

Debnath³

2021

Preprint

View full text Add to dashboard Cite

show abstract

A Study of Conformally Flat Quasi-Einstein Spacetimes with Applications in General Relativity

Abstract: In this paper we consider conformally ﬂat (QE)4 spacetime and obtained several important results. We study application of conformally ﬂat (QE)4 spacetime in general relativity and Ricci soliton structure in a conformally ﬂat (QE)4 perfect ﬂuid spacetime.

Cited by 1 publication

References 19 publications

A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime

A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime

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