[AndroidNeox (OP)]

Suppose you have a Schwarzschild black hole with an event horizon.

I presume that a light beam shone upward from an event horizon would be infinitely redshifted before it travels any distance above the event horizon. The redshift from an event horizon up to any point in space is infinite. This is because the gravitational potential energy difference between an event horizon and any point above the event horizon is infinite.

Conservation of energy requires that gravitational redshift is reversible. Infinite redshift up mean infinite blueshift down. The blueshift a light beam will undergo when traveling from any point in space to an event horizon is infinite.

Thought experiment: Place a laser at some point outside of the event horizon, stationary with respect to the black hole. Point the laser radially downward toward the center of gravity of the black hole. Turn on the laser.

By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted. The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.

This is true no matter where in space the laser is located. Before light can travel from any point in space to an event horizon, infinite time must pass at that point in space. This is also true for every point in space that the light beam travels through on the way to the event horizon. Each of those points can be considered as a light source and infinite time must pass in those points before the light can travel to the event horizon.

If light cannot travel a path in finite time, nothing can. Not matter or energy or information.

It seems to me that this sort of reasoning could be why Einstein insisted black hole event horizons are impossible.

[Bored chemist]

"Is there an error in this relativistic thought experiment?"
Yes.

In principle, it is possible to cross the Event Horizon of a sufficiently massive black hole without noticing.

The change to an infinite blue shift happens at the singularity in the middle; not at the EH.

And we never get to see what happens there. We can safely assume that we shouldn't rely on the laws of physics as we know them.

[AndroidNeox (OP)]

You're wrong about light dilation. Light traveling from a point at higher gravitational energy to lower is blue shifted. It happens between Earth orbit and Earth's surface. It has nothing to do with any singularity.

[David Cooper]

The solution is that the light never quite reaches the event horizon, but slows down to a near halt. The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands). The calculations that suggest that objects can cross the event horizon (and that light crosses it too) are based on the idea that clocks never really slow down, so objects are imagined to go on falling through the event horizon from their own point of view and continue on down to a singularity, but this could only happen after more than an infinite amount of time has gone by for the rest of the universe, which means there are no singularities yet and that all the stuff falling towards a black hole centre is frozen in place at the same distance from the centre as it was when it stopped at where the event horizon was at the time it stopped there. The black holes should evaporate away (due to Hawking radiation) before that material has a chance to move any further in, so in reality most of it can never reach the singularity, but perhaps the light can - as the black hole evaporates, the event horizon will migrate inwards as the energy density just outside the event horizon is reduced, so the light will get a chance to move a bit further in. At some stage when the event horizon disappears and the light is free to to go straight through what was the centre of the black hole, it will be shoot out the other side, liberated, never at any stage being infinitely blue-shifted.

[AndroidNeox (OP)]

The solution is that the light never quite reaches the event horizon, but slows down to a near halt.

Yes, this seems like the only explanation. The only thing it doesn't explain is why people think black hole event horizons can exist.

[Halc]

Suppose you have a Schwarzschild black hole with an event horizon.

I presume that a light beam shone upward from an event horizon would be infinitely redshifted before it travels any distance above the event horizon. The redshift from an event horizon up to any point in space is infinite. This is because the gravitational potential energy difference between an event horizon and any point above the event horizon is infinite.

Not because of that.  The gravitational potential between those two points is finite, but enough for escape speed to be c.  For it to be infinite would violate conservation of energy.

Thought experiment: Place a laser at some point outside of the event horizon, stationary with respect to the black hole. Point the laser radially downward toward the center of gravity of the black hole. Turn on the laser.

By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted.

From the perspective of the point outside the EH, the beam never gets there.  I learned to envision a lot of this by exploring the Rindler horizon, which has most of the same properties. 

The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.

Accelerate a ship at some constant proper rate, and shine a laser (why is a laser necessary?  Will not a candle do?) to the rear, and in the frame of the ship, the light will go only so far.  I suppose it blue shifts to infinity as you put it.  So at 1g of proper acceleration, this limit is just over a light year away, where there is a singularity with something like Hawking radiation and everything, but only in the frame of the accelerating ship.

The light does in fact get there, and beyond.  Rocks really do fall into black holes, with nothing unusual about the event.  No Hawking radiation observed by the rock for instance.  It just doesn't fall into the black hole in the frame of this distant observer is all.

[guest46746]

Disregarding all the reasons cited above, which are all mostly in unison, deter mining of the properties involved in the question may be of value.

If the beam of the laser is pointing downward into the BH, the laser beam is redshifted from the perspective of the observer. From the perspective of the BH, the laser beam is blueshifted via the oncoming beam and the force of gravity attraction from the BH, combined. Are the forces equal at this time?  Does the force of the BH's gravity in conjunction with the incoming laser beam create a blueshift that alters the redshift from the perspective of the observer to a blueshift? At what moment does the dual effect of the from the perspective of the BH, overtake the redshift of the observer?  Physic's at the event horizon may not and probably doesn't match anything we know. What is the dominant perspective? The BH's or the observers? my bet would be on the BH. lol

Can multiple forces working in conjunction overturn physic principles. In this situation can light be sped up to the point of where it alters the light spectum? can an infrared wave light be reversed into a gamma wave light by altering its wave length by force?  lol

[guest4091]

By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted. The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.

What is the source of the unlimited energy?

[Bored chemist]

The solution is that the light never quite reaches the event horizon, but slows down to a near halt. The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands). The calculations that suggest that objects can cross the event horizon (and that light crosses it too) are based on the idea that clocks never really slow down, so objects are imagined to go on falling through the event horizon from their own point of view and continue on down to a singularity, b

That very much depends on your perspective.
It's true from outside the hole.
But not true for the observer falling in.

"Observers crossing a black hole event horizon can calculate the moment they have crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon."
From
https://en.wikipedia.org/wiki/Event_horizon

You're wrong about light dilation. Light traveling from a point at higher gravitational energy to lower is blue shifted. It happens between Earth orbit and Earth's surface. It has nothing to do with any singularity.

I didn't say the light wasn't blue shifted.

I said that the infinite shift you are talking about is not observable from "outside".

[David Cooper]

That very much depends on your perspective.
It's true from outside the hole.
But not true for the observer falling in.

There is only one reality - if the material is evaporated away through the Hawking radiation process before it can progress beyond the point where the event horizon was when that material got stuck there, it cannot also go through an incompatible series of events in which it crosses the event horizon there and continues on down to a singularity. The calculations about it crossing the EV and continuing down to the singularity apply to a time beyond the infinite future for the black hole, and it's only a particular interpretation of GR in which no clocks are allowed to run slow where they are imagined to be able to take a shortcut into the future which can project them further forward into the future than the infinite. That would be an extraordinary trick to perform, but fortunately it doesn't have to do that because all that material will be destroyed (along with the black hole) long before it gets the chance, and that's something that hasn't been taken into account by the people who make claims about how material falls past the event horizon and on down to the singularity - they depend on the black hole lasting for an infinite length of time, and even then the material still can't move any further down towards the singularity, so it needs an infinite number of infinite lengths of time, and even that won't be enough.

[Bored chemist]

The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands).

If nothing ever falls in, how can it expand?

[jeffreyH]

There is a difference between information going into a black hole and information coming out. The escape velocity at the horizon equals the speed of light and points away from the centre of gravity. The clue is in the word escape. Things approaching the horizon will not slow down. Only the signals coming out from those objects slow down. This nonsense about objects never reaching the horizon needs to be shut down. It is simply wrong. Gravity accelerates objects towards the source. It certainly doesn't slow them down. It is the information sent out by the infalling objects that may give this impression.

[Toffo]

The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands).

If nothing ever falls in, how can it expand?

The black hole bends space-time. The stuff over the event horizon bends space-time some more.

The event horizon is a result of all mass in the neighborhood.

[Toffo]

The solution is that the light never quite reaches the event horizon, but slows down to a near halt.

Yes, this seems like the only explanation. The only thing it doesn't explain is why people think black hole event horizons can exist.

Near the center of a neutron star neutrons exchange gluons, the exchange process is slowed down by gravitational time dilation.

Then the neutron star pulls some matter out of a star. Now the gluon exchange process stops completely at some radius from the center of the neutron star. We have a event horizon there.  The event horizon is becoming larger as mass is moving towards the event horizon as the neutron star is shrinking.


(Hmm I guess neutrons do not actually repel by exchanging gluons. Well that's just a small error )

[Halc]

I didn't say the light wasn't blue shifted.

I said that the infinite shift you are talking about is not observable from "outside".

Nobody observes a blue shift.  The guy falling in looks backwards (or forwards to his buddy going in first) and sees both red shifted.  To see a blue shift, you'd have to be stationary and looking up.  That works on the surface of Earth, looking up to the signals from the orbiting stuff, but it doesn't work at the event horizon.  It isn't possible to be stationary there.  It isn't a valid inertial reference frame.

Am I right about that?  One can very much be stationary at the Rindler horizon, but the view from there (looking at the other observer that defines the horizon) is red shifted from both observers.  From the perspective of the outside observer, time does not pass for the observer at the event horizon, yet from the perspective of that (stationary) observer at the horizon, the first guy is red shifted.  Of course being stationary is the equivalent of an observer falling into a black hole.  To be equivalent to being stationary at the black hole, that observer would need to stay stationary relative to the accelerating frame of the first observer, and that perspecitive would make that first observer blue shifted (infinitely so).  So yes, I think I got it right.

Funny that one view has a red shift and the other a blue shift, but time is stopped for both.  That's the problem with playing with an invalid reference frame.  How can one be moving/accelerating without time?

[MikeFontenot]

Suppose you have a Schwarzschild black hole with an event horizon.
[...]

I'm in the tiny minority of people who believe that there is NOTHING beyond the event horizon, that there is no BEYOND the horizon ... i.e., that the event horizon itself is the closest thing to a "center" that a black hole has.

In the Schwarzchild derivation for a spherically symmetric, non-rotating mass, one encounters a quadratic equation in the variables r and t, which produces two solutions for r as a function of t.  One solution clearly corresponds to being "outside" the event horizon (where r >1), because it approaches the Newtonian solution as r -> infinity.  Most people conclude that the other solution (for r < 1) corresponds to the "inside" of a black hole, down to a "center" at r = 0.  But I concluded that the other solution of the quadratic equation is just a spurious mathematical result, with no physical significance (as often happens when quadratic equations arise in physics).  My conclusion was influenced by the fact that for r < 1, the variable r is not the spatial variable, but instead is the time variable.  So r = 0 ISN'T a spatial center, it corresponds to some sort of end of time.  (For r > 1 and large, r behaves like a Newtonian radius in spherical coordinates.  As r approaches 1, it still behaves like a radial coordinate, except that it becomes a nonlinear function of the Newtonian radius.)

I found out, some years ago, that my tiny group of like-minded people contains a very famous person: Paul Dirac come to exactly the same conclusion as mine, back in the 60's, and published a paper (which I read online) to that effect.  I'll take that company anytime.

[David Cooper]

There is a difference between information going into a black hole and information coming out. The escape velocity at the horizon equals the speed of light and points away from the centre of gravity. The clue is in the word escape. Things approaching the horizon will not slow down. Only the signals coming out from those objects slow down.

Do you understand what you're claiming? (1) Are you saying that the speed of light outwards is not the same as the speed of light inwards at the event horizon relative to it? (2) Alternatively though, if you think the speed of light is the same there relative to the event horizon in opposite directions, do you imagine that matter overtakes light in order to cross the event horizon?

This nonsense about objects never reaching the horizon needs to be shut down. It is simply wrong.

I've asked for confirmation of this business here before and the answer appeared to be that the speed of light is the same in all directions at the event horizon relative to the event horizon, so if you want this shut down, someone needs to point to a high-status source that spells out either that the speed of light at the EV relative to the EV is different in opposite directions OR which states unambiguously that matter overtakes light on the way into a black hole.

Gravity accelerates objects towards the source. It certainly doesn't slow them down. It is the information sent out by the infalling objects that may give this impression.

I am not being misled by that issue. The issue here is entirely about what the speed of light is at the EV relative to the EV. If it's the same both ways (i.e. zero), then for matter to cross the EV inwards would be an extraordinary phenomenon (particularly if you think of matter being made up of waves), but if the speed of light isn't the same both ways relative to the EV at the EV, that would also be problematic. I have been trying to establish for a long time what the official position is on this is because if the speed of light is different in different directions there, this must also apply above the EV all the way up through the gravity well, and the same should apply to the gravity well which we are in here.

So, can we settle this issue once and for all instead of having it come back again and again.

[jeffreyH]

The frame of the infalling object is not inertial but if you ignore tidal forces it mimics an inertial frame at very small scales. You are comparing apples and orangutans.

[jeffreyH]

The other point to note is time in the infalling frame. If we drop objects in the earth's gravitational field then the time of release makes a difference. If they are all released simultaneously then they will keep pace with each other. If they are released at intervals then they will not keep pace with each other. In this respect the falling frame appears like an inertial frame embedded in a series of accelerating frames. The objects further away from the source of the field fall behind. This looks like them accelerating away from our frame. The objects closer to the source move away, again looking like they are accelerating away. There is already directional bias. This is the bias caused by the vector direction of the gravitational force. Time is important for objects in the field but not positions within the field. They can be considered static for an idealised field.

[jeffreyH]

The effect on an object depends upon its position within the field and its current velocity. It is the velocity that is time dependent. The position within an ideal stationary field is unaffected by time. This means that time dilation is a function of velocity alone. Gravity acts like a catalyst that only indirectly causes the time dilation.