I Asteroid hits static black hole

[timmdeeg]

Suppose an asteroid hits a static black hole almost tangentially, does this cause rotation of the black hole?

 

[Halc]

An object with angular momentum relative to a non-rotating black hole will result in a black hole with that angular momentum.

 

[Dale]

This case is interesting to me because the non-rotating singularity is spacelike but the rotating singularity is timelike. I have never understood the transition

 

[Ibix]

Remember that a Schwarzschild black hole has zero angular momentum everywhere in all of spacetime. So the asteroid can't exist.

When you've got an asteroid in the spacetime you don't have a static black hole. You may have something that looks very, very like a Schwarzschild black hole, but it is neither Schwarzschild nor Kerr. So I would hang a very large question mark over what the interior looks like.

However, I would agree that you can spin a hole up or down by throwing asteroids at it. The Penrose process is a way of extracting energy from rotating black holes by slowing their spin.

 

[javisot20]

Even a simple photon can make a black hole spin. If we talk about maximally extended Schwarzschild black hole, the Ibix reflection is true, there is nothing that makes the black hole rotate in that case. It is a vacuum solution, pure curvature, there is no matter anywhere.

https://doi.org/10.1103/PhysRevD.14.3260. Page shows that Hawking radiation reduces energy (mass) and angular momentum. Therefore, a Kerr black hole loses angular momento trought Hawking radiation.

(Offtopic: The equations describe the evolution but not what happens at the end of the process. It may be that if loses angular momentun at the same rates as its emits by Hawking. It may also be that in reality it does not happen like that, we do not know yet)

 

[PeterDonis]

This case is interesting to me because the non-rotating singularity is spacelike but the rotating singularity is timelike. I have never understood the transition

I think most physicists believe that the maximally extended Kerr solution, with the timelike singularity inside an inner horizon, is not physically realized, because of the "infinite blueshift" problem at the inner horizon. I think the general belief is that, if there is such a thing as an actual rotating black hole with an outer event horizon (as opposed to the objects we now call "rotating black holes" actually not having any event horizon at all, but only an apparent horizon, i.e., something like a rotating version of the Bardeen model that has been discussed in some previous threads, where the "hole" with its apparent horizon evaporates away and there is never any true event horizon or singularity at all), then the singularity inside ends up being spacelike, like Schwarzschild, because of quantum effects that prevent the inner horizon or what's inside from ever forming. But I don't know of any fully developed model along these lines.

 

[Dale]

I think most physicists believe that the maximally extended Kerr solution, with the timelike singularity inside an inner horizon, is not physically realized, because of the "infinite blueshift" problem at the inner horizon. I think the general belief is that, if there is such a thing as an actual rotating black hole with an outer event horizon (as opposed to the objects we now call "rotating black holes" actually not having any event horizon at all, but only an apparent horizon, i.e., something like a rotating version of the Bardeen model that has been discussed in some previous threads, where the "hole" with its apparent horizon evaporates away and there is never any true event horizon or singularity at all), then the singularity inside ends up being spacelike, like Schwarzschild, because of quantum effects that prevent the inner horizon or what's inside from ever forming. But I don't know of any fully developed model along these lines.

Interesting, so that would sound like actual black holes would have even less "hair" than allowed by the no-hair theorem.

 

[PeterDonis]

that would sound like actual black holes would have even less "hair" than allowed by the no-hair theorem.

The externally observable "hair" would still be the same: mass, angular momentum, and (if present although this would be expected to be extremely rare) electric charge. In other words, the spacetime outside the event (outer) horizon would look the same. The quantum corrections, whatever they might be, would only affect the interior.

 

[timmdeeg]

Remember that a Schwarzschild black hole has zero angular momentum everywhere in all of spacetime. So the asteroid can't exist.

When you've got an asteroid in the spacetime you don't have a static black hole. You may have something that looks very, very like a Schwarzschild black hole, but it is neither Schwarzschild nor Kerr. So I would hang a very large question mark over what the interior looks like.

However, I would agree that you can spin a hole up or down by throwing asteroids at it. The Penrose process is a way of extracting energy from rotating black holes by slowing their spin.

So a non-radial infalling mass into a static black hole just turns to a radial path and then hits the singularity. Nothing else happens. An angular momentum isn't created. Is that correct?

But conservation of momentum holds, right?

 

[Ibix]

So a non-radial infalling mass into a static black hole just turns to a radial path and then hits the singularity. Nothing else happens. An angular momentum isn't created. Is that correct?

But conservation of momentum holds, right?

Basically, dropping anything into a Schwarzschild black hole is similar to bouncing a ball off a wall that doesn't move at all. It's a simplified model that's probably good enough for most purposes, but the simplification loses some momentum (or angular momentum) down the back of the sofa.

Schwarzschild spacetime can't have anything except the black hole. When we use it to model things falling into a black hole we are assuming that the things have zero stress-energy, so have zero effect on the black hole. If you want to consider a black hole that changes in any way then you need a more sophisticated model, and probably a bigger computer than I have. I don't have anything except the most general expectations about what the interior of such a black hole looks like.

 

[timmdeeg]

Schwarzschild spacetime can't have anything except the black hole. When we use it to model things falling into a black hole we are assuming that the things have zero stress-energy, so have zero effect on the black hole. If you want to consider a black hole that changes in any way then you need a more sophisticated model, and probably a bigger computer than I have. I don't have anything except the most general expectations about what the interior of such a black hole looks like.

We can't model that, yes, but besides of that it seems reasonable to conclude, that if an infalling mass is in free fall all the way down then nothing happens regarding angular momentum. But perhaps this is too simple.

 

[Ibix]

I would expect momentum and angular momentum conservation to hold, yes, although there can be nasty surprises. As I noted above, Penrose suggested a way to use a spinning black hole as a giant flywheel and extract its energy.

My point is just that such a black hole isn't really static ever, and suspect that the interior might well look very different to that of a Schwarzschild black hole.

 

[javisot20]

By adding quantum effects to the Schwarzschild black hole it also evaporates, without increasing its angular momentum.

Black holes have three horizons that in the case of Schwarzschild coincide at Rs. They can be stable or unstable, for the Schwarzschild black hole, the Killing vector K = ∂t becomes null at the event horizon.

Killing, event and Cauchy horizons, under certain conditions they stop coinciding at Rs, as is the case with Kerr.

 

[timmdeeg]

I would expect momentum and angular momentum conservation to hold, yes, although there can be nasty surprises.

Ok, thanks.

My point is just that such a black hole isn't really static ever, and suspect that the interior might well look very different to that of a Schwarzschild black hole.

Perhaps with the mass in a yet unknown state of high density in the center.

 

[Ibix]

Perhaps with the mass in a yet unknown state of high density in the center.

@PeterDonis would know better than me, but as I understand it the singularity theorems imply that non-trivial spacetimes always have singularities somewhere under fairly general circumstances. So I'd expect a singularity, just not necessarily a similar geometry to the interior of a Schwarzschild black hole.

 

[PeterDonis]

Black holes have three horizons

No, two. If there is a Killing horizon at all (which requires that the hole is perfectly stationary), it coincides with the event horizon.

 

[PeterDonis]

So a non-radial infalling mass into a static black hole just turns to a radial path and then hits the singularity.

No. If there is a non-radially infalling mass that is non-negligible, then the spacetime as a whole does not have zero angular momentum and hence cannot be Schwarzschild.

In other words, the whole idea of modeling something with non-negligible angular momentum (as well as mass) falling into a "static black hole" cannot be done using one idealized black hole solution. You have to do a messy numerical simulation.

 

[PeterDonis]

Perhaps with the mass in a yet unknown state of high density in the center.

There is no such thing, at least not if I am correct about what you mean. See below.

as I understand it the singularity theorems imply that non-trivial spacetimes always have singularities somewhere under fairly general circumstances. So I'd expect a singularity, just not necessarily a similar geometry to the interior of a Schwarzschild black hole.

The singularity theorems say that if you have a spacetime containing a trapped surface in which the energy conditions are obeyed everywhere, then that spacetime must be geodesically incomplete. "Geodesically incomplete" is the precise technical definition of "has a singularity". Note that the theorems do not say that any invariants must increase without bound as the finite limit points along incomplete geodesics are approached; in other words, it does not have to be the case that anything "goes to infinity" at a singularity. In cases where that does happen, it has to be established by specific computations using that specific spacetime geometry (for example, computing curvature invariants as $r \to 0$ in Schwarzschild spacetime).

The two key conditions of the theorems are often not fullly considered. The first condition, it should be noted, is not that an event horizon is present--it is only that a trapped surface is present. In an idealized model like Schwarzschild spacetime, the trapped surface is the same as the event horizon. But that is not generally true. There are models that have trapped surfaces, but no event horizons anywhere.

The second condition, that the energy conditions are obeyed everywhere, are satisfied by what we think of as "matter" and "radiation", but they are not satisfied by dark energy (aka a cosmological constant), or by certain quantum field states. There are models like the Bardeen "black hole" (a misnomer, as will be evident in a moment) which have trapped surfaces, but no event horizon and no singularity anywhere (i.e., they are geodesically complete), because the stress-energy tensor in the deep interior acts like dark energy and violates the energy conditions.

So if we are looking for a model of something that looks from the outside like a black hole, but has some kind of "yet unknown state" of mass in the deep interior, that state cannot be any kind of ordinary matter or radiation. It can only be something like the Bardeen solution. But that solution has no event horizon and is not a black hole. There is no way to have both an event horizon and some kind of ordinary matter or radiation in the deep interior that is stationary.

 

[javisot20]

Let's not forget, and possibly going off topic, for modern science a certain black holes is a certain quantum system, for example, https://arxiv.org/abs/0809.4266

 

[PeterDonis]

Let's not forget, and possibly going off topic, for modern science a certain black holes is a certain quantum system, for example, https://arxiv.org/abs/0809.4266

This is a speculative hypothesis, not a generally accepted theory. Discussion of it would be long in the Beyond the Standard Models forum.

 

[timmdeeg]

There is no such thing, at least not if I am correct about what you mean. See below.
..............
So if we are looking for a model of something that looks from the outside like a black hole, but has some kind of "yet unknown state" of mass in the deep interior, that state cannot be any kind of ordinary matter or radiation. It can only be something like the Bardeen solution. But that solution has no event horizon and is not a black hole. There is no way to have both an event horizon and some kind of ordinary matter or radiation in the deep interior that is stationary.

I don't get that yet. And I'm not sure, if we talk about the same thing. Please correct what follows:

There are two "types" of black holes, the "mathematically" founded Schwarzschild black holes and the black holes in our universe formed by gravitational collapse of matter. Would you agree that in the latter case a singularity doesn't exist? And if yes, that some unknown equivalent of the matter should exist?

 

[PeterDonis]

There are two "types" of black holes, the "mathematically" founded Schwarzschild black holes and the black holes in our universe formed by gravitational collapse of matter.

Not really, no.

Our mathematical models of the gravitational collapse of an object like a star to a black hole still make use of the Schwarzschild (or Kerr) spacetime geometries. Those geometries just aren't the entire spacetime; the models don't make use of the full maximal extension of Schwarzschild or Kerr. They only make use of a portion of that.

Also, as far as the objects in our actual universe that are formed by gravitational collapse, that we currently refer to as "black holes", are concerned, we don't know exactly what they are. To know for sure that a particular object is a true black hole, i.e., that it has a true event horizon, you would have to know the entire future of the universe, since "event horizon" is a global property of the entire spacetime, which includes the entire future. But of course we don't and can't know the entire future.

Would you agree that in the latter case a singularity doesn't exist?

No. We don't know exactly what is inside the objects that we currently call "black holes".

that some unknown equivalent of the matter should exist?

"Equivalent of matter" means "obeys the energy conditions", and as I said, anything that obeys the energy conditions will do no good at all in getting around the singularity theorems. What is needed to do that is an equivalent of dark energy, not matter. In other words, any model of an object that looks to us from the outside like a black hole, but actually isn't one--has no true event horizon and no singularity--has to have something like dark energy in its deep interior. As I said, we know quantum fields can in principle have such effects, but we don't know enough about them to be able to construct a detailed model of how such effects would happen in a gravitational collapse.

 

[javisot20]

(I remenber reading about that in this piece, it's in Spanish https://francis.naukas.com/2023/02/...erior-explican-la-energia-oscura-cosmologica/)

 

[timmdeeg]

Also, as far as the objects in our actual universe that are formed by gravitational collapse, that we currently refer to as "black holes", are concerned, we don't know exactly what they are.

Ok, understand and thanks for your detailed answer. So we will probably never know for sure if those objects have an event horizon.

Here the result of a quick search:

... As a result, should a star reach such compactnesses, its final fate can only be that of a black hole (This is also known as “Buchdal’s theorem”and applies also for realistic equations of state.).

I don't know, if this conclusion is widely accepted. Only for interest, what is your impression, do physicists in general believe that said objects are black holes?

 

[Ibix]

I don't know, if this conclusion is widely accepted.

The assumption (possibly unstated) in your source is that the energy conditions always apply. In that case, Buchdal's theorem says collapse is unstoppable once the star is 9/8 of a Schwarzschild radius across. But if the energy conditions are violated then collapse can stop, and the Bardeen black hole Peter has mentioned is an example of this. It's not strictly a black hole, but is functionally identical on human timescales (my suspicion is that if such things turn out to be the real answer then the term "black hole" would expand to include them - there's no escape from a black hole even linguistically ).

We believe dark energy exists and violates the energy conditions - so we have circumstancial evidence that such things are possible.

 

[PeterDonis]

we will probably never know for sure if those objects have an event horizon.

We can never know for sure that they do. But at some point we might be able to show that they don't, by finding an alternate model that makes predictions different from the event horizon model, that we can actually test. For example, at some point someone might come up with a Bardeen-like model that makes testable predictions about events outside the trapping horizon, such as some kind of signature of a merger event that is different from the standard GR black hole signature, and which we could possibly observe.

 

[PeterDonis]

I don't know, if this conclusion is widely accepted.

Note the key qualifier: "for realistic equations of state". By "realistic" they mean "obeys the energy conditions". Buchdahl's Theorem assumes the energy conditions, just as the singularity theorems do; if the energy conditions are violated, Buchdahl's Theorem no longer applies.

 

[timmdeeg]

So the open question is whether or not the energy conditions apply. I tend to believe they do but of course that says nothing. Is there any other example in physics (except dark energy) where they don't?

 

[javisot20]

So the open question is whether or not the energy conditions apply. I tend to believe they do but of course that says nothing. Is there any other example in physics (except dark energy) where they don't?

For example Timmdeeg, you may have heard of warp, superluminal warp works with exotic matter that violates the conditions. Miguel Alcubierre wrote 2 articles about warp in 25 years, the first one does not include the analysis of the energy conditions, but the second article does.

1- https://arxiv.org/abs/gr-qc/0009013
2- https://arxiv.org/abs/2103.05610

Alcubierre translates the violation of the energy conditions into the superluminal movement. But it is a theoretical excercise.

 

[timmdeeg]

For example Timmdeeg, you may have heard of warp, superluminal warp works with exotic matter that violates the conditions.

That seems to be a quite exotic example. I'm not sure how seriously one should take that.

 

[PeterDonis]

the open question is whether or not the energy conditions apply

More precisely, whether they apply under conditions of extreme gravitational collapse. As I think I mentioned, certain quantum field states can violate the energy conditions; the question is whether the conditions encountered in extreme gravitational collapse would induce a kind of phase change that would produce such states. That's likely to remain an open question for a long time since that regime is nowhere near being accessible to our experiments any time soon.

 

[javisot20]

That seems to be a quite exotic example. I'm not sure how seriously one should take that.

What you wanted to ask is whether there are more examples in nature of non-compliance with the conditions. The example I gave is within theoretical physics, as I said, and they are exact solutions of Einstein's equations.