Cygnus X-1 is nearly extremal.

[bcrowell]

Gou et al., "The Extreme Spin of the Black Hole in Cygnus X-1," http://arxiv.org/abs/1106.3690

The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black hole's accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a/M>0.97 (3 \sigma). For a less probable (synchronous) dynamical model, we find a/M>0.91 (3 \sigma). Our results take into account all significant sources of observational and model-parameter uncertainties, which are dominated by the uncertainties in black hole mass, orbital inclination angle and distance. The uncertainties introduced by the thin-disk model we employ are particularly small in this case, given the disk's low luminosity (L/L_{Edd} \approx 0.02).

Pretty cool. I'd been under the mistaken impression that real black holes were unlikely to be near the limiting spin.

 

[atyy]

Interesting. Some theorists have been hoping for findings like these.

http://arxiv.org/abs/1103.2355
"For example the lower bound on the ratio J/M2 for GRS1915 + 105 is 0.98. Its mass is known to much less precision; it is estimated to be between 5 and 15 solar masses. The sky contains other candidates for rapidly rotating black holes. For example a measurement of the maximal redshift of the iron line for the supermassive black hole in the center of the nearby Seyfert galaxy MCG-6-30-15 indicates J/M2 is greater than 0.99 [14]. Given the rapid progression of our knowledge of the sky, it is quite possible that more such near-extreme Kerr black holes will be discovered in the near future."

 

[cephron]

Please pardon the noob question - a google search of "black hole limiting spin" turned up some things, but not the information I was looking for - what is a black hole's "limiting spin"? Would a black hole exceeding this spin speed be (according to some) a naked singularity? Or is it an asymptotically unreachable limit related to c? Something else entirely?

 

[atyy]

Please pardon the noob question - a google search of "black hole limiting spin" turned up some things, but not the information I was looking for - what is a black hole's "limiting spin"? Would a black hole exceeding this spin speed be (according to some) a naked singularity? Or is it an asymptotically unreachable limit related to c? Something else entirely?

http://en.wikipedia.org/wiki/Kerr_metric#Overextreme_Kerr_solutions

I don't know if that's true (just ignorant), but they do reference Chandrasekhar. I'd be very interested to know if this is indeed a naked singularity solution of GR.

 

[bcrowell]

Would a black hole exceeding this spin speed be (according to some) a naked singularity?

I believe there simply can't be a black hole exceeding this limit. I think if you try to toss any more angular momentum into it, the particles just won't go in.

A black hole definitely can't evolve into a naked singularity by absorbing normal matter; that would be a trivial counterexample to cosmic censorship, and I'm sure there are no such trivial counterexamples.

[EDIT] The statement above is too strong. See #7-8.

 

[Ben Niehoff]

This is pretty cool.

As for "limiting spin", one can find some relations among the various parameters that describe a black hole such that they resemble thermodynamics. They are identified as follows:

Mass -> Internal energy
Hawking temperature -> Temperature
Horizon area -> Entropy
Angular velocity, Electric potential -> Chemical potentials
Angular momentum, Electric charge -> Particle counts conjugate to the chemical potentials

Since the same math as thermodynamics shows up, the same laws apply. One is that the horizon area is always increasing. Another is that absolute zero temperature is not reachable by any physical process. Extremal black holes have zero Hawking temperature, so there is no physical process that can "spin up" a black hole to the $a = m$ limit.

 

[atyy]

I believe there simply can't be a black hole exceeding this limit. I think if you try to toss any more angular momentum into it, the particles just won't go in.

A black hole definitely can't evolve into a naked singularity by absorbing normal matter; that would be a trivial counterexample to cosmic censorship, and I'm sure there are no such trivial counterexamples.

There's discussion about this in http://arxiv.org/abs/gr-qc/9808043 and http://pirsa.org/11050063/.

 

[bcrowell]

There's discussion about this in http://arxiv.org/abs/gr-qc/9808043 and http://pirsa.org/11050063/.

Interesting paper -- thank! If you click the "cited by" link on the paper, it turns out that there's a ton of recent work on this, with four or five papers, all seemingly reaching contradictory conclusions, coming out within the last six months.

BTW, the interesting case seems to be the one where it's charged and you overcharge it (not the one where it's electrically neutral and spinning and you overspin it). This probably doesn't connect to realistic astrophysical black holes, which are electrically neutral.

[EDIT] Here are some notes from the Poisson talk:

Veronika Hubeny, 1998 "Overcharging a Black Hole and Cosmic Censorship," http://arxiv.org/abs/gr-qc/9808043

critical collapse; Choptuik, 90's; spherical collapse of a scalar field; massless naked singularity; requires infinite fine-tuning of initial conditions

black string in 4+1 dimensions; if string is long enough, initial perturbation creates instability, black-hole beads connected by filaments; naked singularity

main topic of rest of talk is Hubeny's mechanism, generalized to rotating case

charge of b.h. is O(e^2) away from extremality; particle has mass and charge O(e)

if assume test charge, you can definitely make a b.h. initial state end up in a state where its mass and charge are super-extremal; presumably this object will be a naked singularity

but analysis is inconclusive because need to include electromagnetic self-force; Hubeny knew this

Poisson says they now know how to calculate self-force

a spherical shell bounces back, so that scenario isn't a possible counterexample

sign of self-force is not obvious in the sense of helping censorship or working against it

tricky arguments involving the membrane picture, treat as conductor, use image charges to calculate self-force

the self-force doesn't drag, it does positive work on the particle while also feeding energy into radiation; is counterintuitive, goes against naive statement of cons of energy; (29:57) there is a third form of energy besides mechanical energy and EM radiation; the only way you can reduce it to these two forms is for periodic motion; otherwise there's a total-derivative term that isn't negligible

gets back to the same issue of the e.p. and falling charges, Bryce deWitt

complicated numerical calculation; infinite sum that needs to be renormalized

only did calculations for trajectories in which particle falls from rest, not Hubeny trajectories; result is that (1) self-force is outward, just like force from black hole; (2) self-force increases with the charge of the black hole

next, will do calculations for Hubeny trajectories

is willing to bet that they will soon have proof that cosmic censorship is saved from Hubeny scenario

 

[martinbn]

Sorry to bump this thread up, but it is very interesting, and I just found that in the paper cited above by atyy, http://arxiv.org/abs/gr-qc/9808043, there is a reference to a paper by Wald "Gedanken Experiments to Destroy a Black Hole", which is a nice read and treats these questions in detail.