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

**Authors:** Stephen J. Crothers

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.

**Comments:** 6 pages.

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### Submission history

[v1] 3 Jan 2011

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