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

Stephen John Crothers
Year: 2005
Keywords: Kepler's 3rd Law, Vacuum Field, Point-Mass
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.