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Complete Exterior and Interior Solution of Einsteins Field Equation using the Riemannian Golden Metric Tensor for Homogenous Spherical Massive Bodies with a Field that has a Variation in Radial Length and Time} |
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PP: 59-64 |
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doi:10.18576/sjm/120301
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Author(s) |
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A.I. Ode,
I.I. Ewa,
L.L. Iwa,
J.S. Iwa,
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Abstract |
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| In the theory of general relativity, the Einsteins field equation is a tensor field equation which described the geometry of space-time to the distribution of matter within it. These equations were constructed in a form of tensorial field which relate the local space-time curvature with the energy, momentum and stress around that space. In this research work, the Riemannian geometry of space-time was applied to obtain fourteen component of affine connection coefficients, Riemann Christofell tensor, Ricci tensor and exterior Einsteins field equation for spherical field and find solution in form of power series. The result obtained yields a function $f(t,r)$ to the order $c^{0}$ reduces to Laplacian equation , implying that it agrees with the well-known equivalence principle in Physics and to order of $c^{-2}$ it contains post Newtonian additional correctional terms which are not found in Newtons dynamical theory or Einsteins geometrical theory of gravitation. The consequence of the additional correctional terms is that it can be applied in the detection of the existence of gravitational waves. The interior solution was obtained for a static homogeneous spherical bodies whose tensor field varies with time and radial distance was constructed and solved. It was observed that within the interior field, the solution obtained converges to Newton dynamical scalar potential which is thus an extremely discovery with the reliance on two arbitrary function. The result obtained in the limit of weak field is equal to Laplacian equation which does not differ significantly from Newton dynamical theory of gravitation. The solution further confirms the assumption that Newton dynamical theory of gravitation is a limiting case of Einsteins geometrical gravitational theory of gravitation. |
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