Modification of the Exterior and Interior Solution of Einstein’s g22 Field Equation for a Homogeneous Spherical Massive Bodies whose Fields Differ in Radial Size, Polar Angle, and Time

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dc.contributor.authorRilwan, Usman
dc.contributor.authorMaisalatee, A.U.
dc.contributor.authorOgwu, E.I.
dc.contributor.authorOkara, O.G.
dc.contributor.authorMuhammad, S.
dc.contributor.authorUbaidullah, A.
dc.contributor.authorAbdulrahman, H.
dc.date.accessioned2023-12-14T07:51:46Z
dc.date.available2023-12-14T07:51:46Z
dc.date.issued2021-08-16
dc.description.abstractIn general theory of relativity, Einstein’s field equations relate the geometry of space-time with the distribution of matter within it. These equations were first published by Einstein in the form of a tensor equation which related the local space-time curvature with the local energy and momentum within this space-time. In this article, Einstein’s geometrical field equations interior and exterior to astrophysically real or hypothetical distribution of mass within a spherical geometry were constructed and solved for field whose gravitational potential varies with time, radial distance and polar angle. The exterior solution was obtained using power series. The metric tensors and the solution of the Einstein’s exterior field equations used in this work has only one arbitrary function f(t,r,θ) , and thus put the Einstein’s geometrical theory of gravitation on the same bases with the Newton’s dynamical theory of gravitation. The gravitational scalar potential f(t,r,θ) obtained in this research work to the order of co, c-2 , contains Newton dynamical gravitational scalar potential and post Newtonian additional terms much importance as it can be applied to the study of rotating bodies such as stars. The interior solution was obtained using weak field and slow-motion approximation. The obtained result converges to Newton’s dynamical scalar potential with additional time factor not found in the well-known Newton’s dynamical theory of gravitation which is a profound discovery with the dependency on three arbitrary functions. Our result obeyed the equivalence principle of Physics.en_US
dc.identifier.citation1. Green, B. R. (2004) The Fabric of the Cosmos, Alfred, A. Knopf, Random Publication House Inc. New York. Pp 38-40. 2. Howusu, S. X. K. (2010) Einstein’s Geometrical Field Equations, Jos University Press Ltd., pp 34. 3. Chifu, E.N.& Howusu, S.X.K.(2009) Solution of Einstein’s Geometrical Field Equations Exterior to Astrophysical Real or Hypothetical Time-Varying Distributions of Mass within Regions of Spherical Geometry,Progress in Physics,3: 45-48. 4. Chifu, E. N. (2012) Gravitational Fields Exterior to a Homogeneous Spherical Masses. The Abraham Zelmanov Journal, 5: 31-67. 5. Lumbi, L. W., Ewa, I. I. & Tsaku, N. (2014) Einstein’s Equations of Motion for Test Particles Exterior to Spherical Distributions of Mass whose Tensor Field Varies with Time, Radial Distance and Polar Angle. Archives of Applied Science Research Library. 6(5): 36-41. 6. Chifu, E.N. (2009). Astrophysical Satisfactory Solutions to Einstein R33 Gravitational Field Equations Exterior/ Interior to Static Homogenous Oblate Spheroidal Masses, In Proceedings of 3rd International IMBIC Conference, 75-89.en_US
dc.identifier.urihttps://keffi.nsuk.edu.ng/handle/20.500.14448/6026
dc.language.isoenen_US
dc.publisherDepartment of Physics, Nasarawa State University Keffien_US
dc.subjectEinstein’s field equation, radial distance, polar angle, Schwarzchild’s metric, gravitationen_US
dc.titleModification of the Exterior and Interior Solution of Einstein’s g22 Field Equation for a Homogeneous Spherical Massive Bodies whose Fields Differ in Radial Size, Polar Angle, and Timeen_US
dc.typeArticleen_US

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