Are there any known non-rotating black holes

[Lucas_Jackson]

I was reading an interesting article on photon spheres…

A photon sphere is a spherical region just outside a black hole’s event horizon where gravity is so intense that light (photons) is forced to travel in circular orbits. Because spacetime is extremely warped, emitted light loops around the black hole rather than traveling in straight lines or escaping into deep space.

And there was a mention of non-rotating black holes. A first thought is that conservation of angular momentum would prevent them. Googling around a bit I found this opinion…

Implausible and unlikely. But not entirely impossible, because angular momentum is conserved. So two equal but opposite black holes (or neutron stars) can merge and negate each other’s spin (or charge) to an immeasurably low level (even if not absolute zero). And as statistically improbable as that is, considering the sheer number of stellar black holes (and neutron stars) in the observable universe, it may actually be inevitable (within a certain degree of measurement)

My factual questions:

1. Have we detected a non-rotating black hole?
2. Would we even be able to know (since black holes are all but invisible)
3. Do all black holes have photon spheres?

[Chronos]

For the first two questions, it depends on how finely you’re defining. Angular momentum isn’t quite a continuous quantity, due to quantum mechanics, but on astrophysical scales, where typical angular momenta are many orders of magnitude greater than \hbar, it might as well be. While in principle a black hole could have an angular momentum of exactly 0 (or maybe exactly \hbar/2; I don’t know if they’re fermions and/or bosons), in practice the smallest angular momentum we could even hope to measure would be much, much greater than that.

Measuring the angular momentum of a black hole itself could be done by measuring how light propagates around it, or, if it’s closely orbiting something of similar mass, from the details of the gravitational radiation from the system. In practice, though, what we directly detect is usually the matter in the vicinity of the hole which is accreting into it. The angular momentum of the accretion disk is probably closely related to that of the hole, but they can differ a little.

Models predict that most black holes that form should have very high angular momentum, typically around 90% of the maximum possible angular momentum (in appropriate units, the angular momentum is around 0.9 M^2). There’s no reason why holes can’t exist with lower angular momentum (either forming from the collapse of something rotating slowly or not at all, or canceling out from later accretion), it’s just hard to come up with a practical process that leads to them. I don’t think there have been any measurements of black hole angular momentum significantly below the expectations.

And yes, all black holes have photon spheres, which are defined by what light in those regions would do. They may or may not actually have any photons within that photon sphere: You could in principle have a black hole sufficiently isolated from everything else that it’s completely dark.

[Lucas_Jackson]

Thanks, informative.