Derivation of Laplacian Equation from Exterior Einstein Geometrical Field Equation Using Golden Metric Tensor Approach in Weak Field Limit

A.I. Ode^1*, I. I. Ewa², S. R. Tukur², S. J. Kwuko², J. S. Iwa¹, L. L. Iwa³ and M. A. Aliyu¹

The laplacian equation is a second –order partial differential equation which is useful for the determination of the electric potential in free space or region. In this article, the Riemannian geometry of space-time was applied to obtain affine connection coefficients, Riemann christofell tensor, Ricci tensor and exterior Einstein’s field equation for spherical field. The result obtained in the limit of weak field reduces to laplacian equation which agrees with the concept of general relativity, and has a gravitational scalar potential of two functions, 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 Einstein’s geometrical gravitational theory of gravitation.

Keywords : Riemannian geometry, laplacian equation, golden metric tensor, gravitational scalar potential.

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Citation: Ode, A. I. et al., (2025). Derivation of Laplacian Equation from Exterior Einstein Geometrical Field Equation Using Golden Metric Tensor Approach in Weak Field Limit. I J T C Physics, 6(3):1-4.
DOI : https://doi.org/10.47485/2767-3901.1065