# I What problems would 'black holes' not being formed solve?

#### Chronos

Gold Member
You need to look hard at GR to understand why Einstein concluded a singularity is needed in order for an EH to form. He wa pretty bright for a crusty old turn of the century kind of guy.

#### DarkStar42

You need to look hard at GR to understand why Einstein concluded a singularity is needed in order for an EH to form. He wa pretty bright for a crusty old turn of the century kind of guy.
and if you take a collapsing star, the singularity would form at the centre, right? And the event horizon would expand from there as the star fell into it..

But why would a singularity form at all? As time dilation rose, then the matter compressing in the area would rise, slowing compression. I don't see how time dilation could ever reach infinity at any point, like I said, as matter at the centre compressed, the process would slow down, and prevent infinite time dilation occurring and hence a singularity..

#### russ_watters

Mentor
But why would a singularity form at all? As time dilation rose, then the matter compressing in the area would rise, slowing compression. I don't see how time dilation could ever reach infinity at any point, like I said, as matter at the centre compressed, the process would slow down, and prevent infinite time dilation occurring and hence a singularity..
Setting aside the singularity itself, which is essentially thought to be a math error (but it isn't possible to know for sure), there is nothing to stop the formation of the event horizon. Time dilation is not a local phenomena, so locally a particle falling toward the event horizon just passes through it without even noticing. There is nothing to *actually* stop the collapse, it only *appears* to stop to remote observers.

...I'm also seeing (though I'm not a physicist), that the infinite time dilation at the event horizon vs a remote observer only applies to a stationary point (under extreme acceleration) at the event horizon, not someone/thing falling in.

This is a subject that has been discussed before on PF and seemed to make the rounds a few years ago because I think Stephen Hawking said something provocative about it. But it isn't considered to be a real issue for the theory.

#### Nugatory

Mentor
I don't see how time dilation could ever reach infinity at any point, like I said, as matter at the centre compressed, the process would slow down, and prevent infinite time dilation occurring and hence a singularity..
Thinking in terms of time dilation pretty much guarantees confusion because time dilation is a consequence of your choice of coordinates; you can make it come or go or be finite or infinite just by choosing different coordinates (that is, your convention for labeling points in spacetime) to describe what's happening to the infalling matter. The fallacy in using time dilation to show that the singularity cannot form is similar to the fallacy of trying to use time dilation to show that the event horizon cannot form.

No matter what choices you make here and no matter what the time dilation is, when you solve the equations of general relativity (the Oppenheimer-Snyder solution would be a good start - Google for it) for a sufficiently large mass of collapsing matter you'll end up with a singularity.

It is possible that something happens to prevent the singularity from forming, but if so we don't yet have any theory abut what that something might be. For an analogy, we could consider Coulomb's law for the force between two charged point particles: $F=Q_1Q_2/r^2$. Everyone is comfortable with his law and we know that it's good physics - yet it has a singularity at $r=0$. The conclusion we draw from this is that Coulomb's law is a good description of the physics when $r$ is not equal to zero, and it's a mistake to try using it when $r$ is zero; and likewise the singularity that general relativity finds at $r=0$ in a black hole is just telling us that general relativity does not provide a complete description of conditions there.

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#### alantheastronomer

DarkStar42 said:
I find it more intuitive to imagine an object conserving it's angular momentum if it remains an actual object.
Black holes DO conserve their angular momentum - they're called "Kerr black holes" and their event horizons are oblate, bulging out along their equator due to their extreme rotation. There's also a region outside the event horizon called the "ergosphere" where space itself is induced to take part in the rotation in a process called "frame dragging"! If you're interested, there's a section on Kerr black holes on Wikipedia.

#### alantheastronomer

https://en.wikipedia.org/wiki/Magnetospheric_eternally_collapsing_object

"...He argued that all proposed black holes are instead quasi-black holes rather than exact black holes and that during the gravitational collapse to a black hole, the entire mass energy and angular momentum of the collapsing objects is radiated away before formation of exact mathematical black holes ... Mitra argues that he has proven that the world-line of an in-falling test particle would tend to be lightlike at the event horizon, independent of the definition of "velocity"."
According to this article, Mitra claims that gravitational collapse is halted by radiation pressure, it reaches it's Eddington limit. But accreting neutron stars are supported, not by gas pressure or radiation pressure, they are not blackbodies, but by what's called "degeneracy pressure" the pressure due to the neutrons having to be in different energy states according to the "Pauli Exclusion Principle" and not collapsing in on themselves. The accretion proceeds until it's radius exceeds the Schwarzschild radius and an event horizon is formed. If "the entire mass energy and angular momentum of the collapsing object is radiated away" then the object has evaporated and nothing is formed!

#### mathman

some other collapsed object.
If "some other collapsed object" has enough mass and small enough volume so the escape velocity is greater than c, call it what you want - it is a black hole by definition. The open question is - what is the physics inside the event horizon.

#### Dale

Mentor
I would think at least the information loss problem, and then there is the conservation of rotational momentum, and then there is the production of the magnetic field.
I don’t think any of these are actually problems. The information loss problem was famously resolved already and the other two were never problems to begin with.

#### Ilythiiri

But accreting neutron stars are supported, not by gas pressure or radiation pressure, they are not blackbodies, but by what's called "degeneracy pressure" the pressure due to the neutrons having to be in different energy states according to the "Pauli Exclusion Principle" and not collapsing in on themselves. The accretion proceeds until it's radius exceeds the Schwarzschild radius and an event horizon is formed. If "the entire mass energy and angular momentum of the collapsing object is radiated away" then the object has evaporated and nothing is formed!
I posted MECO link as argument against singularity, not event horizon.
Mitra tries to explain BH interior - stuff inside even horizon. In this case neutron/strange star gains enough mass to form event horizon, then accretes some more, radiates away it's mass-energy(by gravitational interaction and Hawking radiation) and loses event horizon roughly by the time last proton decays (:
Without forming singularities along a way.

As absolute zero temperature can't be achieved, same with state of matter within BH - it can approach singularity asymptotically but not reach it (my attempt to wrap my head around BH interior without discarding causality, not a fact).

When i accepted event horizon not as a barrier but rather as something like stable orbit around Earth - meaningful but intangible, necessity of singularity in the center of BH somehow also lost it's plausibility to me.

You need to look hard at GR to understand why Einstein concluded a singularity is needed in order for an EH to form. He wa pretty bright for a crusty old turn of the century kind of guy.
Still, GR is an approximation. Today there also are pretty bright guys standing on the shoulders of giants, doing quite good with quantum physics.

OP, sometime ago i wanted to post a question "is it possible to add angular momentum to Kerr BH and expand it's radius, thus effectively diluting it's mass to the point event horizon vanishes". Then i did my homework - read up most of PF BH related discussions(took several weeks), and didn't.
Later i found "... Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum. Specifically, if the angular momentum is high enough, the event horizons could disappear. ..." part.
I recommend it to you, the reading up part - I found some answers/ideas to questions I haven't figured to ask yet.

Also, a great quote from PF: "I think the biggest misconception about black holes is that physicists agree on what they are. I know of no example of mainstream physics literature where the experts in the field disagree more completely than on the topic of what goes on inside an event horizon." (:

#### DarkStar42

I don’t think any of these are actually problems. The information loss problem was famously resolved already and the other two were never problems to begin with.
I thought Hawking Radiation, Hawking concluded, contained no, or too little, information from inside the event horizon..?

#### DrStupid

No matter what choices you make here and no matter what the time dilation is, when you solve the equations of general relativity (the Oppenheimer-Snyder solution would be a good start - Google for it) for a sufficiently large mass of collapsing matter you'll end up with a singularity.
Is that still the case when Hawking radiation comes into play?

Mentor

#### Nugatory

Mentor
Is that still the case when Hawking radiation comes into play?
Yes. Hawking radiation is a phenomenon associated with the event horizon not the singularity; and it doesn't affect the collapse at all.

#### DrStupid

Yes. Hawking radiation is a phenomenon associated with the event horizon not the singularity; and it doesn't affect the collapse at all.
Do you have a corresonding reference?

#### mathman

Singularity formation is a result of applying General Relativity without taking into account quantum theory. As I have said before, no one really knows what is happening inside a black hole. Until these two theories are reconciled we just won't know.

#### Dale

Mentor
I don’t think that statements objecting to the formation of the singularity are considered particularly controversial. Singularities also appear in other classical theories and so far have been eliminated by the corresponding quantum theories.

Objections to the formation of the event horizon are certainly more controversial.

#### sophiecentaur

Gold Member
depends whether the 'body of science' is an Egyptian pyramid or a space elevator..
Those are both examples of Technology and not 'the body of Science' but the same sort of thing applies. In the times of the Pharos, anyone trying to build a pyramid in a different way from the 'established' way would very likely have run out of time or money - unless there was some significant brilliance on the part of the designer. Plenty of attempts at new technology failed in the past due to \lack of respect' for what was known already.
A space elevator has not yet been built and there may never be a successful one. 'Lack of respect' would be at work if the project was attempted at any time soon.

#### Zedertie Dessen

This question amounts to "if the laws of physics did not apply, what would the laws of physics say about <insert nonsense of your choice>?"
Yes, that is pretty much what I thought. I think the OP question can still be valuable in that regard, if only as a kind of recreational thought experiment. For example, in a universe where the speed of light was variable and increased in the area around a collapsing massive object, wouldn't the event horizon radius keep shrinking? Or vice versa. And so on.

And although those scenarios would all be contrary to known facts, I guess one problem (as the OP asked) that might be solved that way - or rather than solved, would not even exist - would be the black hole information paradox, right? But as you suggest with your comment above, if the physics were different to start with then who knows if the lack of the black hole information paradox would have any value.

Finally, perhaps the OP is hinting at past discoveries that started from apparent impossibilities, such as square roots of negative numbers leading to imaginary number math. I have no training in physics so can't even speculate on whether thought experiments regarding a universe where black holes don't form could lead to any discovery comparable to imaginary/complex numbers.

#### phinds

Gold Member
I have no training in physics so can't even speculate on whether thought experiments regarding a universe where black holes don't form could lead to any discovery comparable to imaginary/complex numbers.
Well, the problem is that if black holes didn't form then General Relativity would not hold, which would require a HUGE change in the entire way the universe works so it would not be some single change at all and we don't have a clue what it would look like so speculating about it isn't really helpful.

#### Dale

Mentor
would be the black hole information paradox, right?
We already discussed that above, it has already been resolved for some time now. As far as I know there is no current problem which would be resolved.

#### zonde

Gold Member
there is nothing to stop the formation of the event horizon. Time dilation is not a local phenomena, so locally a particle falling toward the event horizon just passes through it without even noticing.
This seems to be quite popular argument but it is obviously faulty as it assumes conclusion. So Nugatory's suggestion to google for Oppenheimer-Snyder solution is the right way to go.

Googling for OS solution I found criticism of this solution: Gravitational collapse without black holes. It points toward Penrose for the argument of event horizon formation: "In particular, Penrose (Phys. Rev. Lett. 14:57, 1965) showed that [OS] metric gave rise to trapped surfaces, that is regions of space from which no light rays can escape, and proved that within such surfaces black-hole formation is inevitable."

#### russ_watters

Mentor
This seems to be quite popular argument but it is obviously faulty as it assumes conclusion.
Please be more specific, because I see no assumed conclusion, only a conclusion that logically follows from the starting premises.

Indeed, it looks to me like Nugatory said exactly what I did.

#### zonde

Gold Member
Please be more specific, because I see no assumed conclusion, only a conclusion that logically follows from the starting premises.
In first sentence you talk about formation of event horizon, but in second sentence you talk about particle falling towards already formed event horizon.

"What problems would 'black holes' not being formed solve?"

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