There is no theoretical reason that a non-rotating black hole cannot exist, and in fact the Schwarzschild metric (the simplest exact model of a black hole) is exactly that. In reality, all matter in the universe is in some degree of large scale rotational motion in addition to any arbitrarily defined volumes of mass having net differential linear off-axis motion (creating a net gravitational torque on the masses), so the the likelihood of material converging to form a direct collapse black hole would exactly cancel out net angular momentum is practically nil. Stellar mass black holes form from the remnants of stars, and because of the way star systems form they have significant rotational motion, so any black hole that forms from a collapsar will have substantial angular momentum by default.
The math certainly exists to describe one. And you don’t even have the “pick a random real number” problem, since angular momentum is quantized. Sure, going from a ring singularity to a point one would be weird, but then, going from not-a-singularity to any sort of singularity is also weird.
I don’t see why. A point singularity is just the limiting case of a toroidal singularity with a radius of zero, just like a Schwarzschild black hole is the limiting case of a Kerr black hole, one with a spin rate of zero.
No, but the ‘outer ergosphere’ of a spinning black hole is a weird shape something like a red blood cell, with dimples and everything. This might be one possible source of confusion.
The ergosphere is not in any sense a horizon: You can dip into the ergosphere and come back out again. But you can’t stay still in the ergosphere: If you try, you’ll end up falling. And the ergosphere is also where you can dump your garbage from profitably.
That may just mean that at some level of resolution that spacetime is not continuous. General relativity, as good as it has been in predicting the behavior of gravity in many extreme or subtle conditions, is almost certainly not a complete theory of gravity.
There’s also no real topological obstruction to this happening. Think, for example, of a horizontal plane slicing through a hollow sphere to produce a circle. As the plane rises, the circle shrinks to become a point just when the plane reaches the north pole. Nothing discontinuous going on in this picture. But a circle, with a hole, transitions to a point.
What is the theoretical basis for a black hole retaining electric charge? Is is derived from GR or from theories of particle physics? In the model where charged particles interact by exchanging virtual photons it seems that charge within an event horizon would not be able to interact with external particles (unless virtual photons do not move through spacetime as real photons do).
Electric charge is a conserved quantity due to a symmetry of nature present in the fundamental laws as we understand them today. Matter going from “not a black hole” to “black hole” doesn’t undermine that charge conservation, so whatever charge was there must still quantitatively be in effect, even if qualitatively one has to be careful in the treatment due to spacetime being all jacked up.
This approach to electrodynamics isn’t applicable to a charged black hole, or really any macroscopic object. The concept of virtual photons stems from a calculation approach whereby a discrete interaction can be connected quantitatively to an infinite series; where the terms in that series can be connected to the famous Feynman diagrams involving both real and virtual particles (the latter of which are a echo of the calculation taking place); and where, in many important cases, the calculation is dominated by the first term or so in the series. For electromagnetism, the first term’s diagram will usually involve a virtual photon.
However, this approach and the corresponding heuristics assume many things that do not hold even a little bit in the black hole case. The black hole is not a point-like object, nor is it small compared to the incoming particle’s wavelength such that its physical extent can be handled via a suitable “form factor” or other integration. The technique also assumes that the incoming and outgoing particles are fully free of the localized interaction, whereas the black hole would involve continuous scattering (in curved spacetime no less) of the incoming and outgoing particle states.
Fortunately, classical treatments are generally applicable, even if cumbersome given the context.
A combination of GR and Maxwell’s equations. Above my education level, but charged (non-spinning) black holes were addressed early on:
If I’m reading this correctly, essentially the space-time that a black hole is made of embodies the electric charge. Interestingly, charge is something that can defeat an event horizon: a maximally-charged black hole would have a naked singularity.
A super-maximally charged black hole. One with charge equal to mass (in the appropriate units) is allowed (at least, allowed to exist, but there’s no known method for producing one). One with charge greater than mass would be naked.
What’s perhaps more relevant than electric charge is magnetic charge, which black holes can also have. This is relevant because we don’t know of any other context in which magnetic charge can exist. And in principle, we even know how to make them: Just produce a strong enough magnetic field that it polarizes the vacuum into oppositely-charged black hole pairs.
I believe so. There’s been theoretical proposals in the past to manipulate small black holes (assuming they exist) by giving them a charge and moving or spinning them using it.
Thanks, all. I had not known that GR equations incorporated electro-magnetism. So even though the original charged particles themselves are not observable, the charge itself would remain as an observable feature of the spacetime/EM-field along with mass and spin.
It’s not precisely that the GR equations incorporate electromagnetism. Rather, we know how electromagnetism works in the context of GR. Roughly speaking, the ordinary equations of electromagnetism have a bunch of commas in them (which has a very specific meaning, in that system of notation), and GR says that you can take any such equation and replace all of the commas with semicolons (that also have a very specific, and very closely related, meaning). In other words, if you already know in detail how to describe a given electromagnetic situation in flat space, it’s really easy to adapt that to describing it in curved space.
And I guess a black hole formed from merging objects needs their spin and relative velocity to cancel out to a very unlikely precision. (I mention velocity because normally objects spiral in when forming a black hole, and I guess some of the angular momentum of the black hole comes from that?)
It should be possible to artificially make a black hole of arbitrarily low angular momentum though.
