## Four Poission-Laplace Theory of Gravitation (I)

**Authors:** G. G. Nyambuya

The Poisson-Laplace equation is a working and acceptable equation of gravitation which is mostly used or applied in its differential form in Magneto-Hydro-Dynamic (MHD) modelling. From a general relativistic standpoint, it describes gravitational fields in the region of low spacetime curvature as it emerges in the weak field limit. For none-static gravitational fields, this equation is not generally covariant. On the requirements of general covariance, this equation can be extended to include a time dependent component, in which case, one is led to the Four Poisson-Laplace equation. We solve the Four Poisson-Laplace equation for radial solutions, and apart from the Newtonian gravitational pole, we obtain four new solutions leading to four new gravitational poles capable (in-principle) of explaining e.g. the rotation curves of galaxies, the Pioneer anomaly, the Titius-Bode Law and the formation of planetary rings. In this letter, we focus only on writing down these solutions. The task to show that these new solutions might explain the aforesaid gravitational anomalies, has been left for separate future readings.

**Comments:** 5 Pages. Two Full Research Papers on the Pioneer Anomaly and the Titius-Bode Law will follow this reading. These follow up papers put flesh to the theory here set-forth.

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### Submission history

[v1] 2012-05-31 08:17:57

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