On the Generalisation of Kepler's 3rd Law for the Vacuum Field of the Point-Mass

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Scientific Paper
Title On the Generalisation of Kepler\'s 3rd Law for the Vacuum Field of the Point-Mass
Author(s) Stephen John Crothers
Keywords Kepler's 3rd Law, Vacuum Field, Point-Mass
Published 2005
Journal Progress In Physics
Volume 2
Pages 70-75


I derive herein a general form of Kepler?s 3rd Law for the general solution to Einstein?s vacuum field. I also obtain stable orbits for photons in all the configurations of the point-mass. Contrary to the accepted theory, Kepler?s 3rd Law is modified by General Relativity and leads to a finite angular velocity as the proper radius of the orbit goes down to zero, without the formation of a black hole. Finally, I generalise the expression for the potential function of the general solution for the point-mass in the weak field.