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Dale

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What is the mass of an electron made of?

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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.What is the mass of an electron made of?

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martinbn

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

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

In violation of several laws of physics?It's tempting to say that all the particles disappear down a black hole!

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1what is the mass of a black hole made of? Would it be made of the neutrons (and protons, electrons) that formed the earlier star?

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 isI think mass is not made of anything, but instead it's a mathematical property that particles have when interacting with the Higgs field.

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

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.what happens to those particles? Where do they go to after the black hole is formed?

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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?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 isnotthe 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.

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?According to classical GR, [the particles] hit the singularity at the center of the hole and are destroyed

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Nugatory

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

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Because in this case two fermions would occupy the same state... but by Peter Donis,Why would you think that the exclusion principle might be violated?

so, maybe, they are destroyed before occupying the same state?According to classical GR, they hit the singularity at the center of the hole and are destroyed

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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.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?

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.

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GR is a classical theory so it doesn't treat these aspects at all. Matter is treated as a continuous substance.In this case, the Pauli Exclusion Principle would certainly be violated, no?

We could if we had a theory of quantum gravity. At this point we don't. We only have various speculative candidates.Dont we can use Quantum Mechanics to try to get an idea of what happens there in the singularity?

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Thank youGR 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.

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I think what you may have meant is what

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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.

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a singularity is the point where all physics laws break down.Oh Ok. What is the singularity from a math point of view? Metric assuming the value infinity?

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##

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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?)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##

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Ibix

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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.

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I appreciate your post indeedWhat 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.

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Why don't we aswer the question by "The mass of a black hole is made of matter-energy compounds that formed it, whatever the matter made of due to particle physics"?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 isnotthe 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.

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Because that doesn't address the issue of the multiple possible meanings of the term "mass". Nor does it address the fact that the black hole is vacuum.Why don't we aswer the question by "The mass of a black hole is made of matter-energy compounds that formed it, whatever the matter made of due to particle physics"?

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Like Ibix said a coordinate singularity is just a bad choice we made.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?)

But for the Schwarzschild metric which is a solution to the Einstein field equations and describes the vacuum outside of spherical mass distributions, the metric element contains two singularities ##r=0## which is an essential singularity like I said and ##r=R_{sch}= 2M## which is a coordinate singularity, where the escape velocity is that of light. Now this radius ##R_{sch}= 2MG/c^2## is called the Schwarzschild radius, but we often talk in geometrized units so ##G=c=1## and it becomes ##R_{sch}= 2M##.

This point is also known as the

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Oh ok. Thank you.Like Ibix said a coordinate singularity is just a bad choice we made.

But for the Schwarzschild metric which is a solution to the Einstein field equations and describes the vacuum outside of spherical mass distributions, the metric element contains two singularities ##r=0## which is an essential singularity like I said and ##r=R_{sch}= 2M## which is a coordinate singularity, where the escape velocity is that of light. Now this radius ##R_{sch}= 2MG/c^2## is called the Schwarzschild radius, but we often talk in geometrized units so ##G=c=1## and it becomes ##R_{sch}= 2M##.

This point is also known as theevent horizonand it is what gives the term "black" in the name of the black holes. Since nothing can escape from that surface these objects appear black, because nothing is emitted. Later on Steven Hawking talked about the phenomenon where in the vacuum outside the black hole pair production happens, when a particle and its antiparticle are "born", so one of these particles gets sucked by the black hole and the other manages to escape and that is like the black hole emits radiation.

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martinbn

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