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Author

Shah Alam Siddiqui

Other affiliations: Aligarh Muslim University
Bio: Shah Alam Siddiqui is an academic researcher from Jazan University. The author has contributed to research in topics: Einstein tensor & Riemann curvature tensor. The author has an hindex of 4, co-authored 4 publications receiving 52 citations. Previous affiliations of Shah Alam Siddiqui include Aligarh Muslim University.

Papers
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TL;DR: In this paper, the relativistic significance of concircular curvature tensors has been explored and the existence of Killing and conformal Killing vectors has been established for spacetimes satisfying Einstein field equations.
Abstract: In the differential geometry of certain F-structures, the importance of concircular curvature tensor is very well known. The relativistic significance of this tensor has been explored here. The spacetimes satisfying Einstein field equations and with vanishing concircular curvature tensor are considered and the existence of Killing and conformal Killing vectors have been established for such spacetimes. Perfect fluid spacetimes with vanishing concircular curvature tensor have also been considered. The divergence of concircular curvature tensor is studied in detail and it is seen, among other results, that if the divergence of the concircular tensor is zero and the Ricci tensor is of Codazzi type then the resulting spacetime is of constant curvature. For a perfect fluid spacetime to possess divergence-free concircular curvature tensor, a necessary and sufficient condition has been obtained in terms of Friedmann-Robertson-Walker model.

38 citations

01 Jan 2010
TL;DR: In this article, a study of conharmonic curvature tensors has been made on the four dimensional spacetime of general relativity and the existence of Killing and confor- mal Killing vectors on such spacetime have been established.
Abstract: The signiflcance of conharmonic curvature tensor is very well known in the difierential geometry of certain F-structures (e.g., complex, almost complex, Kahler, almost Kahler, Hermitian, almost Hermitian structures, etc.). In this paper, a study of conharmonic curvature ten- sor has been made on the four dimensional spacetime of general relativity. The spacetime satisfying Einstein fleld equations and having vanishing conharmonic tensor is considered and the existence of Killing and confor- mal Killing vectors on such spacetime have been established. Perfect ∞uid cosmological models have also been studied.

13 citations

Journal ArticleDOI
TL;DR: In this paper, the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal η-Ricci solitons with torse-forming vector field were studied.
Abstract: In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal η-Ricci soliton with torse-forming vector field ξ. Condition for the...

12 citations

01 Jan 2010
TL;DR: In this paper, the divergence of the space-matter tensor has been studied in detail and perfect-fluid spacetimes with divergence-free space matter tensor are considered.
Abstract: The divergence of the space-matter tensor has been studied in detail and the perfect-fluid spacetimes with divergence-free space-matter tensor are considered. It is seen that such spacetimes either satisfy the vacuum-like equation of state or represent a Friedmann-Robertson-Walker cosmological model with (μ−3p) as constant. The space-matter tensor has also been expressed in terms of projective, conformal, conharmonic and concircular curvature tensors and the relations between their divergences have been obtained.

4 citations


Cited by
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Book
01 Jan 1970

329 citations

Journal ArticleDOI
TL;DR: The projective curvature tensor is an invariant under geodesic preserving transformations on semi-Riemannian manifolds and possesses different geometric properties than other generalized curvatures as mentioned in this paper.
Abstract: The projective curvature tensor is an invariant under geodesic preserving transformations on semi-Riemannian manifolds. It possesses different geometric properties than other generalized curvature ...

26 citations

Journal ArticleDOI
01 Sep 2019
TL;DR: In this paper, geometrical aspects of perfect fluid spacetime with torse-forming vector field are described and conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
Abstract: In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field $$\xi $$ are described and Ricci soliton in perfect fluid spacetime with torse-forming vector field $$\xi $$ are determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.

21 citations

Journal ArticleDOI
TL;DR: In this article , the authors studied the relativistic space-time with a torse-forming potential vector field, and evaluated the characterization of the metrics when the space time with a semi-symmetric energy-momentum tensor admits an η1-Einstein soliton, whose potential field is torseforming.
Abstract: The present research paper consists of the study of an η1-Einstein soliton in general relativistic space-time with a torse-forming potential vector field. Besides this, we try to evaluate the characterization of the metrics when the space-time with a semi-symmetric energy-momentum tensor admits an η1-Einstein soliton, whose potential vector field is torse-forming. In adition, certain curvature conditions on the space-time that admit an η1-Einstein soliton are explored and build up the importance of the Laplace equation on the space-time in terms of η1-Einstein soliton. Lastly, we have given some physical accomplishment with the connection of dust fluid, dark fluid and radiation era in general relativistic space-time admitting an η1-Einstein soliton.

17 citations