Why event horizons cannot form

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AndroidNeox

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Why event horizons cannot form
« on: 23/12/2015 22:25:36 »
Einstein accepted that black holes, gravitational collapsars, are inevitable, but he insisted to the end of his life that event horizons are impossible. The reason they are impossible is they would require infinite time to form. Here, I present a simple thought experiment showing why they cannot form in finite time. I begin with the assumption that a Schwarzschild black hole does exist and then show how nothing, not even light, can travel from any point in spacetime to the event horizon.

Consider a gedankenexperiment with a platform, stationary with respect to the black hole. On the platform are a laser, a winch, and two light detectors. The rope payed out by the winch supports a mirror. The laser beam reflects on the mirror and is returned to the platform. As the light beam travels downward, it is blueshifted. As it travels up to the platform, it is redshifted the same amount so that when it returns to the platform, it has the same wavelength it had when it left.

The winch will lower the mirror, paying out rope at a constant rate, x m/s.

When the mirror has been lowered to the event horizon, just before it passes beyond the event horizon and the reflected beam goes out, the light beam will have been infinitely blue shifted going down and the return beam will be equally redshifted coming back up. The laser beam will possess an infinite number of light wave cycles. Because the laser generates light waves at a constant and finite rate, an infinite time is required for it to generate this beam. Before the time a light wave from the laser can reach the event horizon, an infinite amount of time will pass on the platform.

Note that the location of the platform and the speed at which the mirror is lowered are irrelevant.
Consider a freely falling object, dropped from the platform. At any time in its descent, it will have some velocity, y(t_0). To show such an object cannot reach the event horizon, redo the experiment with the mirror being lowered at velocity x=y(t_0). Because the falling object is accelerating from zero to y(t_0) and the mirror has been lowered at the velocity y(t_0) for the whole time, the mirror will always be ahead (below) the freely falling object. Because the mirror cannot reach the event horizon in finite time, the falling object cannot.

Space Flow

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Re: Why event horizons cannot form
« Reply #1 on: 24/12/2015 06:58:02 »
First of all I would like to point out that you and a lot of Physicists, are making the same mistake.
The observed clock rate of something approaching an Event Horizon is not the observed physical rate (speed) that something is seen to approach an Event Horizon.

Secondly it appears to me that you are doing a thought experiment that is outside the laws of Physics.

How far out from the Event Horizon do you propose you establish this platform?

Here are some facts to consider;
The Event Horizon of a 3 Solar Mass Black Hole, using [r=2GM/c^2] has a radius of about 9 Kms. That is the point of no return for light.
Traveling outward from the Event Horizon, a 2.5 Solar Mass Neutron Star has a Radius of about 10 Km.
That would represent the point at which anything stationary would be experiencing the surface gravity of a Neutron Star that is only just able to exist as a Neutron star. Any closer, Neutron degeneracy pressure gives up.
Not a good spot for a winching platform.

Traveling further out. A 1.39 Solar mass White Dwarf, Just shy of the Chandrasekhar limit—at which the white dwarf can no longer be supported by electron degeneracy pressure, has a radius of about 1,000 Km.
This according to the laws of nature is the closest that your hovering platform can be and still be made of atomic elements other than Neutrons. This is 991 Kms away from the Event Horizon.

If you were following a Geodesic path into the Black Hole, you could maintain your Atomic Nature all the way to the Event Horizon. The instant you start to resist that Geodesic and hover the above rules come into play.

So we now have a platform with a winch, Laser, Receiver, and some sort of drive system that can keep the platform in place.
Hmmm.... Drive system?
To hover a platform at a fixed distance of 991 Kms above the Event Horizon of a 3 Solar Mass Black Hole, you will need to supply a constant acceleration of 2,523 g. So all the equipment on that platform before lowering anything has to be able to operate under those conditions, weighing 2,523 times what it would at sea level on Earth. That is some technology. I can't even begin to contemplate what this amazing drive system is using for fuel. But anyway this is super tech and somehow this is achieved.
I notice on your diagram a mirror being lowered on a rope.
And we have the same problem as above.
If you try and lower a mirror, this Universe does not allow it. To control lower you have to hold back against the Gravity and just after you start your mirror and rope turn to Neutronium and fall apart.
We could imagine that they were made out of Neutronium in the first place, but even Neutrons can only withstand to 1 Km from the Event Horizon and they fall apart. You can not control lower anything under any circumstances from a hovering platform to the Event Horizon.

If the mirror was dropped, it would follow it's Geodesic and so remain a mirror made out of Atomic Elements, as it very quickly accelerates to the Event Horizon and disappears.
Maybe you could do your laser experiment in that time. The instant the mirror leaves the platform it will start accelerating towards the Event Horizon at 25,000 m/s/s. An acceleration rate that will keep going up as it gets closer,so an accelerating acceleration to it's doom. Still this super high tech mirror will stay lined up with your laser and you can follow it down for the thousand Kms.
But now the laser beam is not returning from a stationary target. The mirror is accelerating away from it at relativistic speeds, adding that phenomenal redshift to the returned beam. Your above experiment doesn't work.
And all this even that far can only be considered for a non-rotating Black Hole.
I don't believe such is actually possible.

So you also state that a free falling mirror can not reach the Horizon at a finite time. This is where you are confusing observed clock-rate on the mirror with observed speed of the mirror from your reference frame.
The two are related but most certainly not the same thing.
You can easily watch the mirror accelerate in the gravity well all the way to the Event Horizon, and see it disappear, without even having to think about what a clock on that mirror did during such journey. The calculations are not hard so you can easily work out it's speed from your reference frame at any point of the fall. Yes the mirror will achieve relativistic speed so it's own Time-rate will almost come to a standstill but as long as your detectors can adjust for the ever lengthening (redshifted) light from the mirror, from your reference frame you will see it disappear at the Horizon shortly after you release it.
Time dilation does not make something falling to an event horizon appear to physically slow down. Only the clock-rate on that something.
We have to remember that for our reference frame the distance is fixed and light has to be seen to travel that distance at the speed of light.
Again it's irrelevant what the clock rate of another reference frame is, only it's observed speed and direction in ours counts for us. The dilated clock-rate is not something we are able to directly observe when something is relativistic to us. We work it out from observed or calculated relative speed.
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jeffreyH

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Re: Why event horizons cannot form
« Reply #2 on: 26/12/2015 14:06:02 »
There you have fallen into a trap for yourself. If the apparent acceleration of an object falling to an event horizon does not appear to slow down for an external observer then in the reference frame of the falling object it will achieve superluminal acceleration since distance over time has to take into account the stretching of spacetime, the resulting extended distance and the time dilation due to the increasing gravitational field strength. This is an issue I have still not resolved. It becomes more obvious in special relativity when using a modified, time reversed Minkowski metric.

Space Flow

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Re: Why event horizons cannot form
« Reply #3 on: 26/12/2015 23:34:24 »
There you have fallen into a trap for yourself. If the apparent acceleration of an object falling to an event horizon does not appear to slow down for an external observer then in the reference frame of the falling object it will achieve superluminal acceleration since distance over time has to take into account the stretching of spacetime, the resulting extended distance and the time dilation due to the increasing gravitational field strength.
And there I suggest that you are also falling into a trap.
You are mixing the effects of SR, (speed and dilation due to speed) and trying to add to them the effects of gravity as per GR.
I am suggesting that the two effects do not add up together. You are either traveling Geodesic, which means you are not resisting the acceleration due to gravity and remain in free fall, in which case to an outside observer you are seen to accelerate and thus your speed is continually seen to be increasing, or you are resisting your geodesic by whatever means and as such feeling all that gravity acting on you, in which case to an outside observer you are not moving in relation to the event horizon and you come under GR for the relativistic effects of the process of feeling that gravity.
I am suggesting that the second scenario is impossible as nothing we know of can resist that amount of gravity, so GR gravity equations do not come into play.
This leaves us with the free fall scenario, and this to an outside observer is a purely SR scenario of speed.
For the observers falling they are always in free-fall but as their speed increases their clockrate slows. They never go superluminal. They never feel any gravity. The GR effects of Gravity never come into the observations or calculations of either outside or falling reference frames.
The falling observers, by the time they become relativistic, which in this environment would not be long after being dropped, do not experience enough time to know or measure anything, let alone going superluminal.
And of course the outside observer sees them quickly reaching a speed very close to the speed of light as they disappear into the event horizon.
An outside observer can see nothing else as the speed of light has to be seen to be constant. There is from the outside observer's reference frame a measurable distance to be covered and light has to be seen to cover that measurable distance in a measurable time at the speed of light. You can not say because a photon's clock is frozen which it is that light is seen to stand still in any situation, so how can you say that an observer traveling at 0.9999999999999999..... the speed of light because that observer's clock is almost frozen that he can be seen to travel at anything other than 0.9999999999990000.... the speed of light.
GR's relativistic effects apply to an observer experiencing gravity. Not to an observer in free-fall.
As an example take the Muon experiments. A Muon created in the Earths upper atmosphere, travel's towards the ground at close to the speed of light. Consequently it's clock-rate is extremely slowed down. On it's way down it also undergoes acceleration due to the Earths gravity. When we work out how far this Muon will travel, GR is not referred to at all. It's speed is all that is necessary to tell us by how much it's clock-rate has slowed, and knowing it's rest lifetime we can work out how far it will penetrate into the Earth before dying.
The fact that it's clock is getting close to stopping does not mean that we see it's movement almost stopping. On the contrary. It's speed is seen to increase a little due to Earths Gravity.

Observed clock rate is inversely proportional to observed speed, especially when falling into a Black Hole. The slower we observe an observer's clock-rate as that observer is falling towards an Event Horizon the faster we observe that same observer's speed at which they fall towards the Event Horizon. Until they very quickly disappear when they reach it.
I know that there is a lot of material out there claiming the reduced clock rate is equivalent in some way to physically slowing down from an outside observer's reference frame, but they are wrong. The mathematics do not support this view. It would only be true for something hovering above an event horizon, and in this Universe at least that is not possible.

Hope that helps..
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Matter tells Spacetime how to Flow; Spacetime tells matter where to go

jeffreyH

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Re: Why event horizons cannot form
« Reply #4 on: 27/12/2015 00:53:48 »
So what distinction to you make between shell observers, freely falling observers and far-away observers? Why would you say the distinctions you make are important?

Space Flow

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Re: Why event horizons cannot form
« Reply #5 on: 27/12/2015 02:57:25 »
So what distinction to you make between shell observers, freely falling observers and far-away observers? Why would you say the distinctions you make are important?
Because the constant speed of light as seen by all observers guaranties that there are differences in what any observer in a different reference frame see's.
An observer here on Earth would view the stationary platform time dilated and length contracted as demanded by General Relativity according to the strength of the gravity that it is stationary in regard to.
By the same token the same observer here on Earth would view the free-falling mirror time dilated and length contracted according to it's speed as demanded by Special Relativity. As it is not feeling any gravitational effects the only way that GR comes into these observations is by the fact that it is seen to accelerate. So the speed would have to be calculated on a step by step mode, no different than a spaceship under a constantly increasing acceleration. The time dilation and length contraction would in this case follow the ever increasing speed curve. But notice that even though time dilation increases to the point that the clock- rate of the mirror almost comes to a standstill from the Earth point of view, the speed at which it approaches the event horizon is always increasing.
From the Stationary platform point of view, it is stationary and the Earth clock rate is going at a hugely accelerated rate because of General Relativity equations in an extreme gravity environment having slowed the platforms clock. When the mirror is released off the platform the platform will see the mirror rapidly accelerate while in free-fall towards the event horizon. This rapid acceleration will translate to time dilation and length contraction of the mirror as it relativistically accelerates to the Horizon. The platform will also see the mirrors clock-rate come to almost a stand still as it at the same time see's the mirrors speed increase.
There will be some important differences.
The distance measured by the Earth observer from the platform to the event horizon will be a lot longer than the distance measured by the platform, which will be a lot longer than the distance seen by the mirror once it hit's relativistic speed towards it.
I could back this up by calculations and give you exact figures, but they may mean nothing if you don't understand and be able to visualise the concepts to start with.
Space and time do very weird things under these conditions just to make sure that the speed of light remains constant in all reference frames. That is the important thing. No matter what everything else has to do will be done. Speed reference will always be the speed of light and it will always remain constant. For this to remain true something can not be seen to come to a standstill at an event horizon. Only the clock-rate does that.
It is irrelevant to an outside observer what the clock-rate of the mirror is doing. Only it's observed speed is relevant.
We have no way to observe the clock-rate of something traveling at almost the speed of light, we can only calculate it from observed speed (SR) or from amount of Gravity it is resisting by standing still at any one point in a Gravity well (GR).
We can theoretically observe either the speed or the amount of Gravity at any point in a Gravity well.

Oh I forgot to m,mention the point of view or reference frame of the mirror.
While on the platform it of course is identical to the platform's. Once dropped over the side, because of the length contraction and time dilation as it very rapidly approaches the speed of light, it would have the experience of a couple of planck intervals of time where the Black Hole Event Horizon would accelerate towards it and reach it at almost the speed of light. If it could differentiate between one Planck instant and the next that is, because that is all the time it would experience.

Hope that helps.
« Last Edit: 27/12/2015 04:32:55 by Space Flow »
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jeffreyH

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Re: Why event horizons cannot form
« Reply #6 on: 27/12/2015 22:16:06 »

The infinitesimal vector displacement is given by

$$dr\,=\,\sqrt{1 - \frac{2m}{r}} dt t + \frac{dr r}{\sqrt{1 - \frac{2m}{r}}} + r d\theta \theta + r sin \theta d\phi \phi$$

This should answer your questions. Apologies but the latex on this forum refuses to put in the unit vector arrows.
« Last Edit: 27/12/2015 22:42:20 by jeffreyH »

jeffreyH

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Re: Why event horizons cannot form
« Reply #7 on: 27/12/2015 22:35:47 »
Shell observers will then measure infinitesimal time using.

$$\sigma^t\,=\,\sqrt{1 - \frac{2m}{r}}dt$$

jeffreyH

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Re: Why event horizons cannot form
« Reply #8 on: 27/12/2015 23:12:51 »
One thing I forgot. Far away observers will see the object falling with speed.

$$\frac{dr}{dt} = - ( 1 - \frac{2m}{r} ) \sqrt{\frac{2m}{r}}$$

Space Flow

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Re: Why event horizons cannot form
« Reply #9 on: 28/12/2015 10:46:23 »
Unfortunately it is the Schwarzschild solution that get's everyone so confused.
Using the Schwarzschild metric will have us working things out using Cartesian Coordinates which unfortunately give us a coordinate singularity at the Event Horizon, giving us answers that include infinities.
Under this metric I would use;  V=(1-rs/r) x sqrt(rs/r x c) where (rs) is the Schwarzschild radius.
This as I said has a problem because the metric runs out at (rs) and returns infinity which has people thinking that nothing can be seen to enter a Black Hole.
Now this is an obvious problem especially if we place a shell observer just above the event horizon. Again using the Schwarzschild solution with the same Cartesian Coordinate System; v= sqrt(rs/r x c) that shell observer would see the in-falling cross the Event Horizon with a velocity of c.
This sort of discrepancy can't exist in a causal system, so we are obviously doing something wrong.
Luckily you and me don't have to solve this. It has already been solved. The Cartesian coordinate system that runs out at the Event horizon is replaced by the Eddington-Finkelstein coordinates. This coordinate system goes through (rs) to a singularity at the centre. Therefore the Event Horizon is represented by finite coordinates that are no different in essence to any other coordinates, outside that radius.
Now distant and shell observers will agree that an in-falling Mass will be seen to get to the Event Horizon at almost the speed of light, and disappear on crossing.
Because an interesting effect of this metric is that for any r that is smaller than rs, all future-directed paths are in the direction of decreasing r.
The surface rs, while being locally perfectly regular, globally functions as a point of no return — once a test particle dips below it, it can never come back. For this reason rs is known as the event horizon;
No event at r ≤ rs can influence any other event at r > rs.
The event horizon is a null surface, not a time-like one.

I do notice that a lot of people including a fair few physicists ignore the causal paradox that Cartesian coordinates bring about in this situation and continue to quote the Schwarzschild solution, therefore claiming that nothing can be seen to enter a Black Hole. I supose it sounds sexier or more mysterious therefore more interesting or something.
All I have to say to that is whenever you end up with infinity in any part of your answer you are doing something wrong.
Infinity is a very valuable conceptual and mathematical tool but; There are no infinities in nature.
« Last Edit: 28/12/2015 10:58:58 by Space Flow »
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jeffreyH

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Re: Why event horizons cannot form
« Reply #10 on: 28/12/2015 12:47:41 »
You do realise of course that the equations I posted take G=c=1 so that 2m IS the value for rs. Once I realised you didn't understand this I stopped reading.

BTW You obviously haven't heard about Kruskal geometry which can extend the Schwarzschild solution to give well defined results at rs (2m).

jeffreyH

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Re: Why event horizons cannot form
« Reply #11 on: 28/12/2015 12:56:35 »
Just in case anyone reading this gets confused, the Schwarzschild solution to the Einstein vacuum equation is the least likely one to occur in nature as the black hole it describes does not rotate. It is a useful model to work with as it is far simpler than models of rotating black holes such as the Kerr metric. Just to dispel any confusion over the word metric, this is a line element.

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

jeffreyH

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Re: Why event horizons cannot form
« Reply #12 on: 28/12/2015 13:20:52 »
Luckily you and me don't have to solve this. It has already been solved. The Cartesian coordinate system that runs out at the Event horizon is replaced by the Eddington-Finkelstein coordinates. This coordinate system goes through (rs) to a singularity at the centre. Therefore the Event Horizon is represented by finite coordinates that are no different in essence to any other coordinates, outside that radius.

I must admit that the Eddington-Finkelstein coordinates do beat the Kruskal–Szekeres coordinates.

https://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates

Neither, however, solve all the problems.

Space Flow

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Re: Why event horizons cannot form
« Reply #13 on: 28/12/2015 20:44:20 »
You do realise of course that the equations I posted take G=c=1 so that 2m IS the value for rs. Once I realised you didn't understand this I stopped reading.
jeffreyH, I did notice that you cut G out of your equations. I also noticed that although my math skills are enough at the moment to give me a geometric understanding, you are much more comfortable with Calculus than my self.

Just in case anyone reading this gets confused, the Schwarzschild solution to the Einstein vacuum equation is the least likely one to occur in nature as the black hole it describes does not rotate. It is a useful model to work with as it is far simpler than models of rotating black holes such as the Kerr metric.
And again this is a good warning for anyone else reading this as I too mentioned initially;
And all this even that far can only be considered for a non-rotating Black Hole.
I don't believe such is actually possible.

As for any system solving all the problems, I think we are a long way from doing anything close to that.
What I have been trying to point out in line with the question posed by this post is that Event Horizons can form, and stuff does fall through them or crushes onto them whichever turns out to eventually be closer to the truth. Either way disappearing from view to any observer outside the rs (2GM)
The mathematics that lead some people to believe that this is not so has a number of problems.

I think that you Jeffrey, are basically agreeing with this view.
Or have I misinterpreted the meaning of your posts?
Either way it has been an interesting discussion and I thank you for it.

We are made of Spacetime; with a sprinkling of Stardust.
Matter tells Spacetime how to Flow; Spacetime tells matter where to go

jeffreyH

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Re: Why event horizons cannot form
« Reply #14 on: 28/12/2015 22:15:54 »
I think that you Jeffrey, are basically agreeing with this view.Or have I misinterpreted the meaning of your posts?

I'm not agreeing with anything.

Space Flow

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Re: Why event horizons cannot form
« Reply #15 on: 29/12/2015 00:42:39 »
I'm not agreeing with anything.
So do you have an opinion on the subject of this thread which is centred around why Event Horizons can not form? ?
« Last Edit: 29/12/2015 00:44:22 by Space Flow »
We are made of Spacetime; with a sprinkling of Stardust.
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jeffreyH

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Re: Why event horizons cannot form
« Reply #16 on: 29/12/2015 01:03:57 »
Scientists and astronomers have been observing Sag A*, the proposed black hole at the centre of the Milky Way. It has not behaved as expected with a gas cloud called G2. That is interesting as it provides data that don't fit expectations. Everything else is speculation.