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Black hole have 3 properties Mass, Charge, Angular Momentum. As there is Angular Momentum it's means black hole is spinning.

  1. How would we know it is spinning in clockwise or anti-clockwise ? (in x,y,+z axis)

  2. Can we place satellite near to black hole above the horizon ?

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    $\begingroup$ What is your definition of clockwise? Related: physics.stackexchange.com/q/55711/2451 $\endgroup$
    – Qmechanic
    Dec 1, 2015 at 13:44
  • $\begingroup$ clockwise and anti-clockwise with respect to x,y,+z axis $\endgroup$
    – gaganyaan
    Dec 1, 2015 at 18:47
  • $\begingroup$ x,y,z axis changes from one observer to another $\endgroup$
    – manshu
    Dec 1, 2015 at 18:59
  • $\begingroup$ @manshu yes i know, i mean + -x,+ -y, only +z . it means we are watching from above. $\endgroup$
    – gaganyaan
    Dec 1, 2015 at 19:33
  • $\begingroup$ how will you find which one is above and which one is below?? $\endgroup$
    – manshu
    Dec 1, 2015 at 19:38

2 Answers 2

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Black hole spin can be estimated by remote observations, but the inclination of the rotation axis, and therefore whether it is spinning "clockwise" or "anti-clockwise" is ambiguous. i.e. The same observational signature is seen for both, since we cannot spatially resolve the accretion disk around the black hole.

The measurements that give the black hole spin are X-ray spectra that reveal doppler shifts in iron lines emitted from the hot inner parts of the accretion discs around black holes. This has been done for stellar-sized black holes (see Lijun et al. 2011) and for supermassive black holes (see Patrick et al. 2012). These measurements suggest that many, but not all, black holes are spinning close to the maximum possible speed allowed by General Relativity.

Yes, in principle "satellites" can orbit black holes. It is orbiting gas that is responsible for the accretion disc emission mentioned above. There is a minimum radius for a stable circular orbit of 3 Schwarzschild radii for a non-spinning black hole.

Things are more complicated for a spinning black hole. Stable, "closed" (i.e. that repeat themselves) circular orbits are only possible in the "equatorial plane". The minimum stable radius is closer or further away than 3 Schwarzschild radii and depends whether the object orbits with or against the black hole spin respectively.

A maximally rotating black hole has a horizon at a radius of half the Schwarzschild radius and this is also the innermost stable circular orbit for a co-rotating satellite.

As Warrick adds in a comment: there may be a way of telling whether the spin is aligned or anti-aligned with the accretion disc orbit (though how the latter case could occur, I don't know), but this cannot tell you the absolute orientation of the spin vector.

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  • $\begingroup$ If memory serves, the accretion dynamics depend on whether the accretion disc is co- or counter-rotating relative to the black hole's spin. So if the accretion disc extends to, say, the innermost stable circular orbit, I think you can work out which way the black hole's angular momentum is aligned. $\endgroup$
    – Warrick
    Dec 1, 2015 at 20:26
  • $\begingroup$ @Warrick You cannot work out which direction the angular momentum vector is, only whether it is aligned or anti-aligned. How you would get an anti-aligned accretion disc evades me. $\endgroup$
    – ProfRob
    Dec 1, 2015 at 21:26
  • $\begingroup$ I only remember it as a theoretical result. The only physical scenario I can think of is if gas is funnelled to a supermassive black hole following a galactic collision and settles down into a disc, it could be aligned differently to the black hole spin. But as you say, this only tells you about the mutual orientation of the black hole and disc. $\endgroup$
    – Warrick
    Dec 2, 2015 at 10:15
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The only sure way to measure the rotation rate of a black hole is to measure the frame dragging it produces on objects near it. Any massive rotating object exerts a torque on objects near it. Even the Earth does this to some extent, though the frame dragging produced by the Earth is so small is is at the limits of measurability. The Gravity Probe B satellite was intended to measure frame dragging by the Earth, but the last I heard it had not produced a conclusive result. The frame dragging by an object massive enough to create a black hole will be easily measurable.

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  • $\begingroup$ Frame dragging doesn't tell you which way the black hole is spinning - not unless you are close! $\endgroup$
    – ProfRob
    Dec 1, 2015 at 16:23

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