Authors : I.Ode; L.W. Lumbi; I. I. Ewa; E. James; I. Kefas

Volume/Issue : Volume 10 - 2025, Issue 6 - June

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Google Scholar : https://tinyurl.com/39yvey8v

DOI : https://doi.org/10.38124/ijisrt/25jun1200

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

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Abstract : In this article, we applied the Riemannian Geometry of space-time and obtained the affine connection coefficient, Riemann Christofell tensor, Ricci tensor and an extended Einstein’s field equation for spherical fields. The obtained result reduces to corresponding pure Newtonian indicating that an agreement with the equivalence principle in Physics. It contains correction term that not in the Newton’s dynamical theory or Einstein’s geometrical theory of gravitation. The consequence of the correction term is that it can be applicable to the determination of the existence of gravitational waves.

Keywords : Riemann Christofell Tensor, Ricci Tensor, Riemannian Theory, Newton’s Theory, Einstein’ Theory.

References :

1. Davis, P. J. (2006). Mathematics & Common Sense: A Case of Creative Tension.
2. Massachusetts: A.K. Peters. p. 86. ISBN 978-1-4398-6432-6.
3. Fock, V. (1966). The Theory of Space, Time and Gravitation (2nd ed.).
4. New York: Pergamon Press Ltd. p. 33. ISBN 0-08-010061-9. Retrieved 14 October 2023.
5. Lawden, D. F. (1982). Introduction to Tensor Calculus, Relativity and Cosmology (3rd ed.).
6. Mineola, New York: Dover Publications. p. 7. ISBN 978-0-486-42540-5.
7. Howusu, S. X. K. (2010). Exact Analytical Solutions of Einstein’s Geometrical                                                                   
8. Gravitational Field Equations, Jos University Press Ltd., 2010, pp vii-43
9. Chifu, E. N. & Howusu, S. X. K. (2009). Solution of Einstein’s geometrical gravitational field
10. equations exterior to astrophysical real- or hypothetical-time varying distributions of mass within regions of spherical geometry. Progress in Physics, 3(4)5-48
11. Chifu, E. N. (2012). Gravitational fields exterior to a homogeneous spherical mass. The           
12. Abraham Zelmanov Journal, 5, 31-67.
13. Gupta, B.D. (2010). Mathematics Physics, Vikas Publishing House PVT LTD
14. Howusu, S. X. K. (2009). The Metric Tensors for Gravitational Fields and the Mathematical   Principles of Riemann Theoretical Physics, Jos University Press Ltd., 19-25
15. Howusu, (2007). S.X.K. The 210 astrophysical solutions plus 210 cosmological solutions of     Einstein’s    geometrical gravitational field equations. Jos University Press, Jos, 6-29
16. Howusu, S. X. K. (2009). The Metric Tensors for Gravitational Fields and the Mathematical   Principles of Riemann Theoretical Physics, Jos University Press Ltd., 2009, 19-25
17. L. W. Lumbi, I. K. Joseph, J. Waida, I. I. Ewa, M. U. Sarki & O. G. Okara (2021). Extension of Some Gravitational Phenomena in Spherical Fields Based on Riemmanian Geometry. Journal of the Nigerian Association of Mathematical Physics. 62, 37-42, ISSN: 1116-4336
18. Maisalatee A.U, Chifu E.N, Lumbi W.L, Sarki M.U. & Mohammed M. (2020)       Solution   of          Einstein’s field equation exterior to a spherical mass with varying potential.  
19. Dutse Journalof Pure and Applied Sciences (DUJOPAS). 2020, 6(2), 294-301. 14    
20. Sarki, M.U., Lumbi, W.L., Ewa, I.I. (2018) Radial Distance and Azimuthal Angle Varying Tensor Field                 Equation Exterior to a Homogeneous Spherical Mass Distribution, JNAMP, 48: 255-260.
21. Rynasiewicz, Robert (2004).  Newton’s Views on Space, Time and Motion
22. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.