# I What is the mass of a black hole made of?

1. Dec 2, 2016

### kent davidge

As the tittle says, what is the mass of a black hole made of? Would it be made of the neutrons (and protons, electrons) that formed the earlier star? If no, what happens to those particles? Where do they go to after the black hole is formed?

2. Dec 2, 2016

### Staff: Mentor

What is the mass of an electron made of?

3. Dec 2, 2016

### kent davidge

Maybe I did not put the right words to describe my question. I think mass is not made of anything, but instead it's a mathematical property that particles have when interacting with the Higgs field.

4. Dec 2, 2016

### martinbn

May be you meant to ask what is the mass of i.e. what does the system with said mass consist of. The answer is that the mass is of the space-time, it can be vacuum no matter is needed. As to the question what happens to the particles, I don't think one can say much i.e. we don't know. By which I mean we don't know (except possibly for conjectures) what the consequences of the theory are. Singularities will form (i.e. there will be geodesicaly incomplete worldlines), but what type they are we don't know. We also don't know which particles will have such worldlines.

5. Dec 2, 2016

### PeroK

It's tempting to say that all the particles disappear down a black hole!

6. Dec 2, 2016

### kent davidge

Oh Ok. What is the singularity from a math point of view? Metric assuming the value infinity?

In violation of several laws of physics?

7. Dec 2, 2016

### Staff: Mentor

The second statement of yours quoted above is easier to answer, so I'll start with that. "Mass" in the sense of what particles get via interaction with the Higgs field is not the same concept as "mass" in the sense of what appears as the constant $M$ in the spacetime metric of a black hole. The first concept is a property of particle interactions. The second concept is a property of the spacetime geometry. So it's important to keep the two concepts separate.

Given that, it should now be easier to see the answer to your first question. The mass of the black hole is a property of the spacetime geometry of the hole. It is not "made of" anything other than that. A better question would be, what causes that property of the spacetime geometry to be what it is? The answer to that question is: the matter and energy that formed the object that originally collapsed to form the hole.

According to classical GR, they hit the singularity at the center of the hole and are destroyed. Most physicists believe that is not what actually happens, because the laws of classical GR no longer work when the spacetime curvature gets strong enough, as it does close to the singularity. But we are not sure at this time what actually does happen in this regime.

8. Dec 2, 2016

### kent davidge

Ok. So is it more correct to say that the Earth's mass, say, is a property of the ST geometry while our own mass is due particle interactions?
In this case, the Pauli Exclusion Principle would certainly be violated, no? Dont we can use Quantum Mechanics to try to get an idea of what happens there in the singularity?

Last edited: Dec 2, 2016
9. Dec 2, 2016

### Staff: Mentor

Why would you think that the exclusion principle might be violated?

10. Dec 2, 2016

### kent davidge

Because in this case two fermions would occupy the same state... but by Peter Donis,
so, maybe, they are destroyed before occupying the same state?

11. Dec 2, 2016

### Staff: Mentor

You're still using a single word "mass" when you should be distinguishing different concepts. If by the Earth's mass you mean, for example, the $M$ that we deduce from measuring the orbital parameters of satellites, the Moon, etc., that is a property of the spacetime geometry. You and I also, in principle, affect the spacetime geometry around us, so we also have a mass in that sense, but it's much, much harder to detect.

If, OTOH, by the Earth's mass you mean the stress-energy associated with all the particles that compose it, that is due to particle interactions--at least, much of it is. There are also contributions from, for example, the kinetic energy of the Earth's atoms, because it is at a finite temperature, the pressure and stresses in the materials that compose the Earth, etc. You and I also have mass in this sense, of course.

So the simple answer to your question is that all objects have mass in both senses; it isn't a question of some having one and some having the other.

12. Dec 2, 2016

### Staff: Mentor

GR is a classical theory so it doesn't treat these aspects at all. Matter is treated as a continuous substance.

We could if we had a theory of quantum gravity. At this point we don't. We only have various speculative candidates.

13. Dec 2, 2016

### kent davidge

Thank you

14. Dec 3, 2016

### smodak

I think what you may have meant is what matter black hole is made of, just as earth is made of several things as described here. I think it is a very interesting question one that I don't believe is so far answered in this thread but I am also curious.

15. Dec 3, 2016

### Stella.Physics

Maybe one should ask where does the mass of a black hole lie. Of course black holes are made of pure spacetime and nothing else; but where exactly does this mass lie, since the matter from the progenitor star is gone and all is left is the singularity and other than that the properties of the spacetime geometry as driven by this new stellar object.

Last edited: Dec 3, 2016
16. Dec 3, 2016

### Stella.Physics

a singularity is the point where all physics laws break down.
For example in the Schwarzschild metric, there are 2 anomalies in the radial coordinate $r=0$ as a pure singularity and another one $r=2M$ but that's just a coordinate singularity.
The Schwarzschild metric is given by
$ds^2 = - \bigg(1- \frac{2M}{r} \bigg) dt^2 + \bigg( 1-\frac{2M}{r} \bigg)^{-1} dr^2 + r^2 d\theta ^2 + r^2 sin^2\theta d\phi^2$

17. Dec 3, 2016

### kent davidge

Very interesting, so the only true singularity occurs at r = 0, but there are more than one coordinate singularity. What happens at these coordinate singularities? (Is it also unknown?)

18. Dec 3, 2016

### Ibix

A coordinate singularity just means you made a bad choice of coordinates for that region. There are coordinate singularities at the north and south poles, but there's nothing odd there in reality.

19. Dec 3, 2016

### phinds

What is at the center of a black hole is called a "singularity" which means "the place where the math model breaks down and we don't know WHAT is going on". It certainly seems likely that whatever is there is broken down into elementary particles but we don't know that and likely won't until there evolves a provable theory of quantum gravity that may (or may not) let us figure out what is likely to be happening at the quantum level.

EDIT: OOPS. For some reason I thought I was responding to a new post and managed to miss the subsequent posts, so I've just duplicated what's already been said.

20. Dec 3, 2016

### kent davidge

I appreciate your post indeed

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