The Kerr-metric is given by

,

where and . We solve the geodesic equation using

It is clear that , then for we obtain the equation

So there is a solution . Next we look to the equation for and we have

An orbit with a constant gives the equation

Thus

So

Now we can write

where . Thus

Then we can write

which can be written as

,

where and . The case gives

,

which reduces to the Third law of Kepler, known as .

The first order of gives

This can we written as

,

this effect is very small and therefore difficult to test by experiment. For the Sun we have , for the Earth we have …

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