There IS no interior of a black hole

That's not what Dirac says, see below.
Mike, I have found Dirac's 1975 book ''General Theory of Relativity''.
Here is a page from that book:
View attachment 5167

https://books.google.co.uk/books?id=7V2YDwAAQBAJ&source=gbs_book_other_versions

* * * * *

r = radius

2m is the Schwarzschild radius.( look-up mass in units of length. It makes things simpler, so they say).

I have underlined where Dirac says things may fall into it.

You may know that r< 2m means radius smaller than Schwarzschild radius.

I spent several months reading that book about a dozen years ago. Only Dirac could write a GR book that's only 69 pages long! The most important thing he said, as far as the current issue is concerned, is this (on page 36):

"The question arises whether such a region [inside the event horizon] can actually exist. All we can say is definitely is that the Einstein equations allow it."

That's certainly not a very strong endorsement for the existence of anything within the event horizon.

That quote above was published in 1975. I think Dirac still doubted that there is anything within the event horizon. I think he maintained that belief because of the way the "r" and "t" variables reversed their natures when going from outside the event horizon to inside the event horizon: "r" is a spatial variable and "t" is a time variable outside the event horizon, but "r" becomes the time variable, and "t" becomes a spatial variable inside the event horizon. That seems absurd to me, and I suspect Dirac had the same view of it. In Dirac's 1962 paper, he said:

"so I feel that the space inside the Schwarzchild radius must belong to a different universe and should not be taken into account in any physical theory." (The "Schwarzchild radius" is the event horizon.)
 
"so I feel that the space inside the Schwarzchild radius must belong to a different universe and should not be taken into account in any physical theory." (The "Schwarzchild radius" is the event horizon.)
Do you understand that a Penrose diagram of a black hole kind of does that? The space is removed, so can't be part of any physical theory--in the future
 
Do you understand that a Penrose diagram of a black hole kind of does that? The space is removed, so can't be part of any physical theory--in the future.

If I've ever seen a Penrose diagram of a black hole, I don't remember it. Does he give that in his "The Road to Reality" book? If not, can you give me another reference for it?
 
"The question arises whether such a region [inside the event horizon] can actually exist. All we can say is definitely is that the Einstein equations allow it."

That's certainly not a very strong endorsement for the existence of anything within the event horizon.
Mike, in 1975 as in 1922, it was still mostly all theoretical about black holes, so Dirac reflects this with ''the question arises whether such a region exist. All we can say definitely is that the Einstein equations allow it.''

''Such a region is called a black hole, because things may fall into it (taking an infinite time by our clocks, to do so) but nothing can come out. '' page 36

What you have to do mike is show where Dirac actually says material is stopped at the event horizon, can you do that?
In other words, give us a quote of Dirac saying that himself,we know you have said it:
It splats onto the event horizon (which is VERY massive).
p36.jpg
 
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The time comment is interesting, though, in the context of the present discussion. Does this start to make sense of Mike's conjecture? If in-falling mass takes an infinite time to collapse inward, to outside observers, can that mean it looks to us as if it is stuck at the edge of the event horizon?
 
If in-falling mass takes an infinite time to collapse inward, to outside observers, can that mean it looks to us as if it is stuck at the edge of the event horizon?
Well....

A remote observer sees an infalling object red shifting and growing ever dimmer as fewer and fewer photons climb up from the EH. Pretty soon, it's just individual ultra-low frequency photons. How long a gap can there be between subsequent photons - and how long can the wavelength be - for it to still be considered "visible"? It's not even enough to form an image at that point. Can we really say we're "seeing an object stuck" at the EH?
 
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Well....

A remote observer sees an infalling object red shifting and growing ever dimmer as fewer and fewer photons climb up from the EH. Pretty soon, it's just individual ultra-low frequency photons. How long a gap can there be between subsequent photons - and how long can the wavelength be - for it to still be considered "visible"? It's not even enough to form an image at that point. Can we really say we're "seeing an object stuck" at the EH?
Why would the number of photons diminish?
 
[...]
What you have to do mike is show where Dirac actually says material is stopped at the event horizon, can you do that?

Dirac said it in his 1962 paper:

"so I feel that the space inside the Schwarzchild radius must belong to a different universe and should not be taken into account in any physical theory."

We know that masses are attracted to a black hole, and accelerate toward a black hole. Dirac says that there is nothing within the event horizon of a black hole, so incoming masses are stopped by the event horizon.
 
Dirac said it in his 1962 paper:

"so I feel that the space inside the Schwarzchild radius must belong to a different universe and should not be taken into account in any physical theory."

We know that masses are attracted to a black hole, and accelerate toward a black hole. Dirac says that there is nothing within the event horizon of a black hole, so incoming masses are stopped by the event horizon.
That is manifestly not what Dirac says at all.
 
[...] your conclusion does not follow from the premise.

My "premise" was:
"Dirac says that there is nothing within the event horizon of a black hole."

My conclusion was:
"so incoming masses are stopped by the event horizon."

We know from observations that masses attracted toward a black hole never stop progressing toward event horizon. We never see them decide to go somewhere else. The premise says that there is nothing inside the event horizon. The only place remaining where they can end up is somewhere on the event horizon itself. Q.E.D.
 
Mike_Fontenot:
I think it says MUCH more than that.
Yes, I know. You already told us that.

In the end, it doesn't much matter what Dirac wrote in one sentence that can be interpreted in different ways, however, unless you place particular emphasis on Dirac as having some special authority when it comes to physics. Science, remember, isn't based on the force of somebody's personality or their prestige.
I think by "different universe", Dirac was literally saying that the equation for r < 1 describes another universe that has absolutely nothing to do with our universe ...
Your conjecture is that no mass passes from our universe to the other universe, or vice versa, if I'm reading you correctly. You think that all the mass falling into a black hole accumulates on the horizon.

The problem I see is that you seem to be relying implicitly on the general relativistic description of a black hole in forming your mental picture of it, while ignoring some of the results from the GR analysis - results discussed by Dirac in some of the references already given.

In the GR description, it is perfectly permissible to use different sets of spacetime coordinates, since the GR description is independent of the particular coordinates chosen. Changing coordinates often just means changing reference frames. One particular choice of coordinates gives us the view of the hole from very far away, as if seen by an observer in "flat" space. But another equally valid choice of coordinates gives us the view of the hole as seen by somebody falling into it, influenced only by its gravity. Using those alternative coordinates, there is literally nothing that distinguishes the event horizon as a special place where mass accumulates, or anything like that. In other words, an infalling observer would not notice anything unusual as she fell through the event horizon. Certainly, she would not hit a wall of matter at the horizon.

Crucially, the physics of the hole cannot depend on the coordinates we use. If there's no wall of matter according to the infalling coordinates, then there can't be a wall of matter at the horizon according to the "flat space" coordinates, either. Note, however, that this by itself says nothing about how the event horizon looks to somebody observing photons travelling away from it. The view of the event horizon from "flat space" (at a distance) is quite different to the view one gets as one falls into the hole. But that's not a problem.
I believe that Dirac believed that NOTHING was inside the event horizon. Or, stated more precisely, that there IS no inside of the event horizon.
I don't think you've managed to find any quote to that effect, so far. But why just rely on Dirac? Why not look at what other experts have to say, as well?
I don't know the answer to that question. Perhaps, the answer is that, calling the event horizon a surface is an abstraction ... an approximation of an actual spherical boundary that has a finite, but very small, thickness. And perhaps, as arriving masses continue to "splat" onto that event horizon, the very small thickness of the event horizon gets very slightly thicker, or maybe just bigger ... i.e., perhaps the radius of the event horizon gets slightly larger, with no increase in thickness.
The challenge you have, as I see it, is to come up with a theoretical model - or better yet, an experimental test - that can distinguish your "solid horizon" hypothesis from the standard "mass contained within a spherical volume" model of a black hole. It looks like you'll need a non-GR model. The main problem, as I see it, is this: what would prevent all of that mass at the horizon from undergoing further gravitational collapse inwards? It seems to me that you'll need to posit some other, non-gravitational, force.
As best I recall (but my memory is fuzzy), that second equation is VERY strange ... it says (I think) that an object falling into the interior of the black hole will end up somewhere on an infinitely long line (not at a point), and it takes an infinite time to get there. (Or maybe that situation is what the new revised equations, which give the perspective of a traveler entering the blackhole, say.)
My understanding is that the positive direction of time inside the event horizon corresponds to motion in space towards the centre of the hole. In other words, since time can't go backwards, any object inside the horizon inevitably moves towards the centre; there's no way to stop that happening, any more than you can stop time from flowing forwards.
 
exchemist:
What I still can't work out, though, is how he thinks the mass of a black hole (a concept that did not exist in his day) exerts its gravitational influence, if the space inside is discarded from any physical theory.
That's actually a valid question even when the space inside is not discarded from the theory.

Remember that the GR description of gravity involves a curving of spacetime. The space around any spherical mass is curved in approximately the same way. The same GR solution applies to the gravity of the Earth or the Sun, for instance, as applies to a black hole.

Mass causes the space around it to curve, which from a distance makes things look as if a force is acting to attract other masses. But gravity isn't a force in the GR description.

The curvature of spacetime around a black hole is caused by the mass of the hole. That doesn't require anything to propagate from inside the hole to the outside. You can imagine the "fabric" of spacetime stretching as more mass is added, like putting a heavy bowling ball on the surface of a trampoline then gradually adding more weight. Even the "space" far from the ball curves more as weight is added. Of course, this is an imperfect analogy.

The gravitational "field" of a black hole is sometimes referred to as a "fossil" or "vestigal" field. Whatever mass caused spacetime outside the hole to curve is no longer visible from outside and it can no longer send any kind of message out from the inside. So, in a sense, it doesn't matter whether the mass is there or not, any more. (Having said that, it appears from Hawking radiation etc. that the total mass-energy of a black hole is conserved, so it looks like whatever mass there is doesn't "go" anywhere inside the hole.)

It's interesting to think about how a black hole can possibly grow as more matter falls into it. I think a good explanation is that as a piece of matter falls in, the event horizon in effect expands outwards towards the infalling matter - just enough to exactly account for the increase of mass related to the infalling matter and simultaneously shielding that matter from view.
The time comment is interesting, though, in the context of the present discussion. Does this start to make sense of Mike's conjecture? If in-falling mass takes an infinite time to collapse inward, to outside observers, can that mean it looks to us as if it is stuck at the edge of the event horizon?
It would look like that, if we could see it. But light emitted outwards from the hole gets more and more Doppler shifted as it comes from closer and closer to the event horizon, until it is infinitely red-shifted at the horizon. So, even though, if we disregard red-shift, it would look from the outside as if all the infalling mass was "stopped" at the horizon, in fact the horizon looks black to us.

But see my post to Mike, above. This "outsider" view of the hole is just one choice of spacetime coordinates - the one we happen to have as observers located at a safe distance outside the hole. A free falling observer would not suddenly find himself surrounded by matter as he fell through the horizon. There is no force that would stop him or anything else falling past the horizon.
Why would the number of photons diminish?
Talking about light emitted from the hole again...

You can actually think of this in one of two ways: using a wave model of light, or a particle (photon) model.

In the wave model, the light waves are stretched out (red-shifted) as they propagate radially outwards. (Again, worth bearing in mind that the physics is the same whether we're talking about the Earth's gravity or a black hole's gravity.) As the waves stretch, their energy decreases.

In the particle model, the number of photons per second emitted by a regular source falling towards the horizon decreases continuously due to gravitational time dilation - time seems to run slower near the horizon than it does far from it. The photons themselves are also "stretched out" as they propagate outwards, again resulting in a red shift of the observed light.
 
Mike, you have claimed the event horzion surface is the ''ENTIRE black hole''.
The event horizon is a surface, and that surface is the ENTIRE black hole.
Note your caps there.

You know that r < 2m means radii smaller than the event horizon.
Here is Dirac saying in 1975 (page 36) that the r < 2m region is called a black hole. My green underlined on page 36 below.
Dirac:
Thus we cannot have direct observational knowledge of the region r < 2m. such a region is call a black hole, because things may fall into it (taking an infinite time, by our clocks, to do so) but nothing can come out.
You're on your own with the idea that the event horizon surface is the ''ENTIRE'' black hole.

p36.jpg
 
I (MikeFontenot) had previously said:

My "premise" was:
"Dirac says that there is nothing within the event horizon of a black hole."

He did not say that.

And it still doesn't follow that - if there were nothing inside - matter would magically pile up on the outside.

In his 1962 paper, Dirac said:

"so I feel that the space inside the Schwarzchild radius must belong to a different universe and should not be taken into account in any physical theory."

I think that is consistent with my above statement that

"Dirac says that there is nothing within the event horizon of a black hole."

In the first quote, Dirac says that nothing beyond the event horizon is a part of our universe. He was saying that anything beyond the event horizon is in some other universe, which has nothing at all to do with our universe, and should be ignored by us.

You (DaveC) said:

"And it still doesn't follow that - if there were nothing inside - matter would magically pile up on the outside."

My reply to that is this:

Any incoming mass (coming straight toward the event horizon) can't reverse course before getting to the event horizon. And it can't stop before it gets to the event horizon. It continues to accelerate toward the event horizon until it hits it. Any incoming mass will be stopped by, and will become part of, the event horizon, making the event horizon larger in diameter, but not thicker. There is nothing to stop the incoming mass except the event horizon.
 
Mike_Fontenot:

In the end, it doesn't much matter what Dirac wrote in one sentence that can be interpreted in different ways, however, unless you place particular emphasis on Dirac as having some special authority when it comes to physics. Science, remember, isn't based on the force of somebody's personality or their prestige.

I've never claimed to know what Dirac's opinion on black holes was, much later in is life. I agree that in his 1975 GR book, he didn't speak as strongly for the non-existence of the interior of a black hole (but he still didn't seem to have much enthusiasm for the existence of the r < 1 region, then either). And I know nothing of his attitude about black holes years after that.

As for myself, until this discussion, I haven't thought about black holes since reading Dirac's treatment, maybe 15 years or so ago). If you look back at my first submission on this topic in this forum, you'll see that I really was only describing my amazement when I accidentally learned from a netnews moderator that my conclusion that there was no interior of a black hole was the same as Dirac's in his 1962 paper (which I hadn't seen up until that time). That was quite a thrill.

I still think the bizarre reversal of the roles of the time and spatial variables ("r" and "t") in Swarzchild's results for the r < 1 region is absurd. And as to the criticism these days for Swarzchild's choice of those coordinates, I think the fact that he chose the r > 1 coordinates to agree with what things look like to us here on Earth was a good choice. I'm also a little suspicious that the new coordinates from the point of view of an infalling person through the event horizon might be a desired solution in search of a problem.
 
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