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Is there a relation between the direction of rotation of black holes or neutron stars and the magnetic dipole moment of BH or neutron stars? BTW, are there different directions of this two parameters for suns?

Edit

I want to be sure there are or there are not the direction of rotation (which one can expressed by an arrow on the rotation axis) and the direction of the magnetic field (expressed by an arrow from the south to the north pole (both arrows are simple conventions)) parallel only. I'm not sure that the direction of the magnetic field is observable at all. And the comment from Zibadawa Timmy about pulsars perhaps a good extension to my question about BH, neutron stars and Suns.

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    $\begingroup$ Pulsars arise when the rotation axis and the magnetic axis are different. If they were the same you'd either see a continuous stream or nothing at all. I'm not knowledgeable enough of the exact mechanics that are thought to explain how this tends to arise, if that's what you're really looking for. $\endgroup$ – zibadawa timmy Feb 7 '16 at 21:41
  • $\begingroup$ @zibadawa Timmy, Nice addition the pulsars. See my edit of the question $\endgroup$ – HolgerFiedler Feb 8 '16 at 4:49
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For pulsars the relation is complex. The magnetic field tends to "freeze in place" after the star collapses, but I'm sure there are all kinds of perturbation mechanisms that may change its initial orientation.

For blackholes (the Kerr-Newman metric, rotating and charged black hole) the relation is very simple: the rotation axis of the BH and the symmetry axis of its magnetic field always coincide.

https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman_metric#Some_aspects_of_the_solution

There is a simple and intuitive justification, although perhaps not rigorous. If the magnetic field was not aligned with rotation, the BH would appear to be "blinking". But a BH cannot "blink", nor can it otherwise send any signals to the external universe. Therefore, its magnetic field axis must coincide with its rotation axis.

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    $\begingroup$ The Kerr-Newman solution is not relevant to real astrophysical black holes, since they are not expected to be charged. The magnetic field that surrounds black holes is expected to be complex and associated with the accretion process. $\endgroup$ – Rob Jeffries Jun 15 '17 at 7:00

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