Abstract
We present the intriguing mathematical and physical similarities arising from the study of the Kerr metric and the Euler's problem of two fixed gravitational centers. We show how one could extend these similarities to physical problems that emerge from the above integrable problems, when both are slightly perturbed.
Highlights
There is an old problem of classical mechanics which is characterized by a lot of properties that are similar to those of an important astrophysical problem; that of a Kerr black hole
The newtonian problem could be used as a simple Newtonian analogue of a Kerr black hole in order to investigate the behavior of the latter one when this is somehow perturbed
If the two masses in the Euler’s problem are not equal, the gravitational field is not reflection symmetric in contrary to what happens with a Kerr black hole
Summary
There is an old problem of classical mechanics which is characterized by a lot of properties that are similar to those of an important astrophysical problem; that of a Kerr black hole. If the two masses in the Euler’s problem are not equal, the gravitational field is not reflection symmetric in contrary to what happens with a Kerr black hole.
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