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To what degree would a non-spinning, non-moving black hole necessarily produce even very weak gravitational waves? Would some be produced as matter/energy reaches it? If so, would no gravitational waves at all be produced if nothing was reaching it, hypothetically? (I suppose these same questions apply to all massive objects.)

A radially symmetric object does not produce gravitational waves, whether it is spinning or not, since it has zero quadropole moment.

> To what degree would a non-spinning, non-moving black hole necessarily produce even very weak gravitational waves?

If it's perfectly non-spinning, and nothing is falling into it, then it emits no gravitational waves at all.

If matter or energy falls in, and does so in a manner that is not spherically symmetric (which will most likely be the case), then some very weak gravitational waves will be emitted. But they will be much, much too weak for us to have any hope of detecting them. Even a gravitational wave detector like LIGO in the same stellar system would have difficulty detecting them.

> As for detecting gravitational waves, except for violent events like black hole mergers, we don't detect any; what few such gravitational waves there are are far too weak for us to detect.

I thought LIGO and VIRGO had been detecting gravitational waves for the last 4 years pretty regularly (i.e. once a week).

Yes, from mergers.

A black hole has a mass, and a volume defined by its event horizon.

From that you can compute a density number, but I agree it's not quite the same concept as the density of water.

> A black hole has a mass

Yes, but not because of "stuff" inside it. As I said, the mass is a global property of the spacetime geometry.

> and a volume defined by its event horizon.

No, it has a surface area defined by its event horizon. But you can't compute a meaningful volume from this surface area. You can, of course, plug the surface area into the formulas of Euclidean geometry, but the number you get will have no physical meaning for a black hole. A black hole has no well-defined volume at all--indeed, one can find spacelike surfaces inside that are infinite in extent, even though it has a finite surface area.

I don’t know if I really agree that a black hole’s mass is not because it has “stuff” (that is, massive entities) inside it. How do you argue that?

In simpler terms, let’s say a star has a mass just below the limit of making it a black hole. Then, a planet collides and it crosses the threshold. Are you saying the “stuff” disappears ?

> How do you argue that?

Because the solutions of the Einstein Field Equation that describe black holes are vacuum solutions. "Vacuum" means "no matter or energy".

> let’s say a star has a mass just below the limit of making it a black hole.

There is no lower limit to the mass of a black hole.

There are maximum mass limits for white dwarfs and neutron stars, and stars more massive than those limits (after they have undergone supernova explosions and probably shed a large portion of their original mass) will collapse to black holes.

As for what happens to the matter in the original object that collapses to a black hole, it reaches the singularity at the center of the hole and is destroyed. But anyone falling into the hole after the collapse will never encounter that collapsing matter; all they will see is vacuum.

We don’t actually know what happens to the matter when it reaches the singularity. Having a singularity effectively means “we don’t know what happens there”.

More precisely, physicists believe that the presence of the singularity in this solution of the Einstein Field Equation means that GR breaks down there and we will need some other theory (the best candidate at this point appears to be a quantum gravity theory) to figure out what happens there. But unless and until we discover that other theory, GR is the best we have and the best we can do is to describe what it predicts and acknowledge the limitations.

I’d argue that GR literally provides no prediction for what happens at the singularity: https://physics.stackexchange.com/a/354893

> I’d argue that GR literally provides no prediction for what happens at the singularity

That's false; GR does make a definite prediction: that curvature invariants increase without bound as the singularity is approached, but that they are finite everywhere in the actual spacetime (see further comments below). (Actually it's more nuanced than that; there are cases where there are incomplete geodesics, which is how "singularity" is actually defined in GR, but not unbounded invariants. But those are edge cases that aren't relevant to what we're discussing here.)

The Stack Exchange thread's claim about geodesic incompleteness is misleading. The actual singularity--heuristically, the "point where things become infinite"--is not included in the spacetime manifold. It is an abstract "boundary point" that is not part of spacetime. What is actually included in the manifold is perfectly well-defined, with nothing infinite anywhere, and is a perfectly self-consistent mathematical model that makes perfectly valid predictions for everything in it.

The Stack Exchange commenter basically doesn't like the fact that GR says "sorry, your model ends here, you can't extend it any further", which is fine, but it's not the same as saying GR must be wrong when it says that. It's just something many physicists are uncomfortable with and so they are looking for a model that doesn't have that property, like quantum gravity. But that's no guarantee that they will find one, nor is it a guarantee that GR must end up being overridden in this regime. It's just a best guess of many physicists at our current state of knowledge. Nor does it mean that GR doesn't make definite predictions; it just means GR's predictions are ones that most physicists would not like having to be stuck with if that's how it turns out. But nature doesn't care what humans like or don't like.

For a proper head spin, consider that gravity propagates at the speed of light... And light is not fast enough to escape the black hole.

https://www.forbes.com/sites/startswithabang/2019/10/24/this...

Light is “fast enough” it just redshifts to nothing. Gravity has no equivalent

> Light is “fast enough” it just redshifts to nothing. Gravity has no equivalent

This is wrong in two ways. First, light at the hole's horizon does not "redshift to nothing"; it just stays at the same radial coordinate because of the curvature of spacetime. The "redshift to nothing" view is an illusion, created by a bad choice of coordinates; that illusion was corrected in the late 1950s and early 1960s by the discovery of better coordinates.

Second, gravity does have an equivalent to light: gravitational radiation. Gravitational waves travel on null geodesics, just like light, and any gravitational waves at the hole's horizon would stay at the same radial coordinate just as light does.

Thank you a lot pdonis for all your explanations along the comments !

You're welcome! :-)

Let’s say there is a light bulb inside the event horizon. It emits a photon. From the light bulb’s perspective, it sees the photon speeding away at the speed of light.

From an outside observer, we never see the photon. It can’t make it out. But — the photon does exist, and it is traveling at the speed of light over a finite (though deeply warped in spacetime) distance. How does the photon not reach us then? Is it not going at the speed of light?

The redshift model applies here; the photon is redshifted until it has no energy from our frame.

> gravity propagates at the speed of light... And light is not fast enough to escape the black hole.

Gravity doesn't have to get out of the hole. The gravity you feel outside a black hole is due to the global spacetime geometry, not to any "force" coming out of the hole. If you want to attribute it ultimately to the presence of matter, it is the matter in your past light cone, which originally collapsed to form the hole, before it fell below the event horizon.

See this Usenet Physics FAQ article:

https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles...

Ya if gravity had to get out of the hole the if a black hole happened in that universe it would just snap shut and kind of disappear.

My understanding is that the black hole curves space so much that there is no path out of it.

This does trap light inside, but speed has nothing to do with it.

No timelike or null path out of it, yes. (That is, no path through spacetime that an ordinary object or a light ray can follow.)