I am curious as to how rapidly most black holes are spinning. A refinement of the question could be: how rapidly are typical supermassive black holes spinning?

I ask because I have the impression that we have not measured the spins of too many black holes, and of the ones we have measured, a significant $\mathcal{O}(1)$ fraction have been spinning at essentially the speed of light, which is to say the angular momentum parameter in the associated Kerr metric would be very close to its extremal bound, $a/M \simeq 1$. For example, a very famous measurement found that the black hole in a binary black hole-star system was rotating at $a/M \geq 0.98$, http://arxiv.org/abs/astro-ph/0606076. I think this measurement surprised people, but I'm wondering if it has now become the rule, rather than the exception. Interestingly, it's much harder to measure the mass than it is $a/M$.

One reason why this is an interesting question to ask, because it concerns possibly the most abundant extractable energy source in the universe. If all black holes are rotating close to extremality, then we or some alien civilation could in principle extract $\sim 29\%$ of their mass-energy via the Penrose-Process. For a solar mass black hole this amounts to far more energy than the Sun outputs in it's lifetime.

And let me self-edit and point out a related post, Are "typical" black holes rotating or static?, but I am asking a slightly different question here. Regarding this previous post, of course typical black holes are rotating (and stationary, as opposed to non-rotating and static), and in fact all physical black holes are rotating to some extent because it is an un-physical idealization to engineer a perfectly symmetric and static collapse scenario that could produce a perfect Schwarzschild exterior.

  • $\begingroup$ Why is it surprising that black holes are spinning near their "natural equatorial velocity"? As matter keeps falling into a black hole it actually has to lose angular momentum just to "get in", which means that most matter will probably enter near the max. angular momentum limit that it can transfer to the black hole to begin with. That seems not much different from any other accretion disk phenomenon. As for the question of extraterrestrial energy needs... I would bet a case of good wine that they are actually rather small. $\endgroup$ – CuriousOne May 13 '15 at 19:43
  • $\begingroup$ Well I'm not at all surprised that most black holes are rotating at an $\mathcal{O}(1)$ fraction of the maximum, but I'm curious about how fast the typical black hole is rotating. Also, I don't follow your argument that most matter that enters is ``near extremal'' itself, that is it's carrying close to the maximum angular momentum per mass. If we swap rotation for charge, then we can certainly add massive uncharged particles to a Reissner-Nordstrom black hole. Are you referring specifically to particles that enter from the equatorial ISCO? $\endgroup$ – Surgical Commander May 13 '15 at 22:36

Black holes need to conserve the angular momentum of all the matter that collapses into them from a spinning star. As the radius of a black hole is considerably less than the radius of the star, it needs a really fast rate of rotation to conserve the angular momentum of all that matter collapsed into a much smaller radius.

Here is an account of the measurement and typical spin rates of 19 supermassive black holes: http://www.nature.com/news/spin-rate-of-black-holes-pinned-down-1.13512. This study found supermassive black holes spinning at from 50% of the speed of light up to nearly the speed of light.

Judging from the prevalence of ellipsoid galaxies in the universe, I'd guess that the black holes at their centers are also ellipsoid, which is an indication of rotation. If black holes at the centers of galaxies are rotating, they likely are rotating very fast, due to conservation of angular momentum for a great mass of rotating material collapsed into a small radius.

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  • $\begingroup$ Ah, thanks very much, that looks like the reference I was searching for! $\endgroup$ – Surgical Commander May 13 '15 at 22:38

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