Surviving the event horizon: some thoughts

In summary: In order to do this, you would have to be able to throw it faster than the speed of light?Yes, in order for the clock to reach the event horizon in one second, it would have to travel faster than the speed of light. However, this is impossible according to the laws of physics. Therefore, the clock would never reach the event horizon in one second and would instead experience a stretched out time as it approaches the horizon. In summary, the concept of crossing the event horizon and experiencing an infinite future is not possible according to the laws of physics. It is more likely that the falling object will experience a stretched out time and will eventually reach the singularity of the
  • #1
ianfort
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So, I remember once watching a lecture series on relativity. In one of the lectures which discussed black holes, the lecturer spoke of what it would be like to actually fall into the black hole. Of course, he did the whole talk about the outside observer seeing the person falling in slowing to a stop as he approached the event horizon, while the person falling in feels himself falling at normal speed for the entire trip. Pretty standard stuff. But then the lecturer said something that somewhat bothered me: if the person were to cross the event horizon, they'd be in the infinite future. Maybe the lecturer was trying to get the point across that anything that goes on beyond is incomprehensible, but the claim is still so illogical I feel it needs addressing. I also would like to propose what the person would actually see when crossing.

Traveling infinity years into the future (or infinity days, or infinity seconds, or infinity anything for that matter) simply doesn't make sense. Certainly time might extend into infinity, that but just means it keeps going. If you keep going, well, you keep going, and going, and going. No matter how long you go on for, you won't be any closer to the end, because there is no end. Leaping an infinite distance in a finite amount of time is akin to finding the last digit of pi. It simply can't happen.

So, then: what does happen when the person crosses the event horizon? Well, to put it simply: he doesn't. I'm pretty sure black holes lose their mass over eons, so as the person approaches the event horizon, it will shrink before their eyes, and finally vanish. In essence, falling into the black hole will transport them to the instant of the black hole's annihilation. If he survived the black hole, he will very likely commit suicide shortly afterward, for everyone he ever knew, and all of the human race in addition, will be gone.

Has this conclusion been proposed before?
 
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  • #2
Probably what your teacher meant was: any (light) signal that the falling observer emits after he has crossed the event horizon, will never reach an observer outside the event horizon. Since we can define "future" as those points in our forward light cone (i.e. whose light signals will reach us at some future time, although that definition would be slightly circular, I suppose) in a sense the faller is in the infinite future, i.e. his light signals will only reach us after infinite time, which is theoreticist-speak for "never".

Since the outside observer will always keep seeing signals from before our unfortunate victim crosses the event horizon (although they will be shifted to longer and longer frequencies and become weaker and weaker), saying that inside the event horizon there is no time is an equally valid (and, IMO, equally ridiculous) claim.

As with more things in relativity, there is no contradiction, but the "explanation" just depends on which viewpoint you take ;)

Note that the "if he survives the black hole" question is irrelevant. GR tells us that after a finite proper time he will reach the singularity, and there is nothing he can do about it (at least, I have done this calculation for a non-rotating black hole, I assume it holds for any variation on that theme).
 
  • #3
It depends.

For small black holes with stellar masses the tidal forces will tear you appart. For huge black holes like in the center of galaxies nothing special would happen at the event horizon.

A very crude estimation is based on Newtonian approximation for the gravitational force. Take the black hole mass M, calculate the Schwarzschild Radius R, derive the gravitational force from F(R) ~ 1/R², and derive the difference F(R)-F(R+L) where L is the typical size of the astronaut or the spaceship.
 
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  • #4
But if the rate at which external time passes approaches a limit of infinity for those approaching the event horizon, and yet the black hole itself will exist for a finite amount of time, wouldn't that mean the person entering would jump to the point in the future where the black hole ceases to exist?
 
  • #5
ianfort said:
But if the rate at which external time passes approaches a limit of infinity for those approaching the event horizon, and yet the black hole itself will exist for a finite amount of time, wouldn't that mean the person entering would jump to the point in the future where the black hole ceases to exist?
There is no objective notion of "external time" in general relativity, and thus no objective statement can be made about what moment in an external's life is simultaneous with some event in the life of the falling observer (like the event of the falling observer crossing the horizon). See the relativity of simultaneity (which says different coordinate systems disagree about which pair of events happened simultaneously, and none are more "right" than the others) and the stuff about "diffeomorphism invariance" in the "equivalent lattices" section of this article (the point being that in general relativity, any arbitrary coordinate system is as good as any other, unlike in special relativity where inertial coordinate systems have a special preferred role). The most common coordinate system to use when introducing nonrotating black holes are Schwarzschild coordinates, where it does take an infinite amount of coordinate time for a falling object to reach the event horizon, but there are other equally valid coordinate systems that can be used in the black hole spacetime where it only takes a finite coordinate time for the falling object to reach the event horizon, like Eddington-Finkelstein coordinates or Kruskal-Szekeres coordinates.
 
  • #6
A fixed observer outside the event horizon will "see" the free falling body crossing the horizon after an infinite time. The proper time of the free falling astronaut (measured on a free falling clock till he/she crosses the horizon) remains finite!
 
  • #7
I would agree with your scenario, strickly as you present it.

speaking as loosly as you were, throw a clock into a black hole. Timed so when it reaches the event horizon it will read 12:00. Retrive it the instant the, as you put it, black hole vanishes.

And i'd bank on it reading close to 12:00 still.

Oh now I understand your post. you're asking

"If he survived the black hole, he will very likely commit suicide shortly afterward, for everyone he ever knew, and all of the human race in addition, will be gone.
Has this conclusion been proposed before?"


OMG no, that's just bizzare. lol just kiding, I know you weren't asking that. but my answer is still true. :)
 
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  • #8
JesseM - "There is no objective notion of "external time" in general relativity, and thus no objective statement can be made about what moment in an external's life is simultaneous with some event in the life of the falling observer (like the event of the falling observer crossing the horizon)."

HUh? what do you think was meant by "external time"? The clock on the wall of the universe?

Clearly "external time" is reffering to the person watching from a distance; from the perspective of the person at the event horizon.
 
  • #9
nitsuj said:
JesseM - "There is no objective notion of "external time" in general relativity, and thus no objective statement can be made about what moment in an external's life is simultaneous with some event in the life of the falling observer (like the event of the falling observer crossing the horizon)."

HUh? what do you think was meant by "external time"? The clock on the wall of the universe?
I think the original poster may have been unaware of the relativity of simultaneity, so may have been intuitively thinking of what would be happening in the external universe "at the same time" as the falling observer was approaching the event horizon.
nitsuj said:
Clearly "external time" is reffering to the person watching from a distance; from the perspective of the person at the event horizon.
But you have to distinguish between visual appearances--what the external observer sees based on light reaching his eyes--and coordinate time in some coordinate system that might be used by the external observer. It's true that visually the external observer would in theory see it take an infinite time for anything to reach the horizon (though as noted here, in reality the object approaching the horizon will eventually appear to disappear because of increasing redshift and the discrete nature of light emission), but then the same would be true for an accelerating observer watching a non-accelerating object approach the observer's Rindler horizon, but in this case I'm sure no one would doubt that the non-accelerating object does cross it since this is a simple SR scenario in flat spacetime, and the object only takes a finite coordinate time to cross it in all inertial reference frames.
 
  • #10
JesseM - No you don't "have to distinguish between visual appearances--what the external observer sees based on light reaching his eyes".

The OPs summary - "In essence, falling into the black hole will transport them to the instant of the black hole's annihilation."

The "Transport them" is what needs your attention.
 
  • #11
ianfort said:
So, then: what does happen when the person crosses the event horizon? Well, to put it simply: he doesn't. I'm pretty sure black holes lose their mass over eons, so as the person approaches the event horizon, it will shrink before their eyes, and finally vanish. In essence, falling into the black hole will transport them to the instant of the black hole's annihilation. If he survived the black hole, he will very likely commit suicide shortly afterward, for everyone he ever knew, and all of the human race in addition, will be gone.

Has this conclusion been proposed before?

The standard view is that an observer can find herself inside the event horizon of an evaporating black hole. Not everyone agrees, however.
George Jones said:
But, as you say, an observer can fall into a black hole in finite time. This means that an observer can find himself inside the event horizon before the black hole evaporates. This is the standard view.

A different opinion appears in a paper by Tanmay Vachaspati, Dejan Stojkovic, Lawrence M. Krauss,

http://www.arxiv.org/abs/gr-qc/0609024 (Accepted for publication in Phys. Rev. D.)

which generated a bit of controversy a few months ago.

Their FIG. 8 is the standard spacetime for an evaporating black hole. Note there is an event horizon, and once across this horizon, an observer cannot avoid hitting the spacelike singularity.

FIG. 9 shows their highly speculative opinion. Note that there is no event horizon and no singularity. This is the main (and controversial) point of their paper: *no* observer (hovering, freely falling, blasting away with a rocket *towards* the surface of the collapsing object, etc.) experiences an event horizon because there is no event horizon to experience.

From the paper: “Instead it may happen that the true event horizon never forms in a gravitational collapse ... The infalling observer never crosses an event horizon, not because it takes an infinite time, but because there is no event horizon to cross. As the infalling observer gets closer to the collapsing wall, the wall shrinks due to radiation back-reaction, evaporating before an event horizon can form. The evaporation appears mysterious to the infalling observer since his detectors don’t register any emission from the collapsing wall Yet he reconciles the absence of the evaporation as being due to a limitation of the frequency range of his detectors. Both he and the asymptotic observer would then agree that the spacetime diagram for an evaporating black hole is as shown in Fig. 9. In this picture a global event horizon and singularity never form. A trapped surface (from within which light cannot es cape) may exist temporarily, but after all of the mass is radiated, the trapped surface disappears and light gets released to infinity.”
 
  • #12
nitsuj said:
JesseM - No you don't "have to distinguish between visual appearances--what the external observer sees based on light reaching his eyes".

The OPs summary - "In essence, falling into the black hole will transport them to the instant of the black hole's annihilation."

The "Transport them" is what needs your attention.
But this is simply wrong in relativity, and in order to explain why I have to distinguish between visual appearances and coordinate systems (and explain about the relativity of simultaneity). Theoretically an external observer will visually see the falling observer reach the horizon at the moment the black hole is annihilated as explained in the last section here, but this is only a delay in the light, the event of the falling observer reaching the horizon happens at a different point in spacetime than the event of the black hole evaporating, and if you use a coordinate system that doesn't have problems at the event horizon such as Kruskal-Szekeres coordinates, you should find that the coordinate time of crossing the horizon is well before the event of the annihilation (although black hole annihilation is actually impossible in "pure" general relativity so knowing the exact curvature of spacetime and creating a coordinate system to describe that spacetime isn't fully possible without a theory of quantum gravity).
 
  • #13
JesseM - that is a very good point.


So is this statement true? "In essence, falling into the black hole will transport them to the instant of the black hole's annihilation."
 
  • #14
nitsuj said:
JesseM - that is a very good point.So is this statement true? "In essence, falling into the black hole will transport them to the instant of the black hole's annihilation."
No. It seems like you didn't really understand my previous post--you quoted that exact same statement last time, and I said "But this is simply wrong in relativity", and gave reasons why:
the event of the falling observer reaching the horizon happens at a different point in spacetime than the event of the black hole evaporating
if you use a coordinate system that doesn't have problems at the event horizon such as Kruskal-Szekeres coordinates, you should find that the coordinate time of crossing the horizon is well before the event of the annihilation
 
  • #15
nitsuj said:
So is this statement true? "In essence, falling into the black hole will transport them to the instant of the black hole's annihilation."

I agree with JesseM, the statement is false. Here's one way of trying to describe, in non-mathematical terms, what is going on:

Say you emit an outgoing light signal at the instant you cross the event horizon of a black hole. That signal will stay at the horizon for as long as the horizon exists (because the horizon is an outgoing lightlike surface). That means that if the black hole is "eternal" (a classical Schwarzschild black hole with no quantum evaporation), your light signal will stay at the horizon forever. If the hole is a quantum hole that eventually evaporates, your light signal (emitted at the instant you crossed the horizon) will stay at the horizon until the black hole evaporates, at which point it will flash outward along with all the other light signals emitted at the horizon (and a light signal emitted at the instant of the hole's final evaporation, which event coincides with the "future endpoint" of the horizon).

But--the above also means that any light signal you emit *after* you cross the horizon will *never* emerge again from the hole, even if the hole evaporates. Instead, all such signals, along with you yourself, will hit the singularity at some point. Even if the hole evaporates (meaning that the singularity eventually disappears), you, and all light signals emitted by you after you cross the horizon, will hit the singularity *before* it disappears. (All this follows from the fact that no event inside the horizon can send light signals to or outside the horizon, and the "future endpoint" of the singularity is a point on the horizon.) So once you're inside the horizon, you're doomed, regardless of the future fate of the hole.
 
  • #16
ianfort said:
But then the lecturer said something that somewhat bothered me: if the person were to cross the event horizon, they'd be in the infinite future. Maybe the lecturer was trying to get the point across that anything that goes on beyond is incomprehensible, but the claim is still so illogical I feel it needs addressing. I also would like to propose what the person would actually see when crossing.

Traveling infinity years into the future (or infinity days, or infinity seconds, or infinity anything for that matter) simply doesn't make sense. Certainly time might extend into infinity, that but just means it keeps going. If you keep going, well, you keep going, and going, and going. No matter how long you go on for, you won't be any closer to the end, because there is no end. Leaping an infinite distance in a finite amount of time is akin to finding the last digit of pi. It simply can't happen.

So, then: what does happen when the person crosses the event horizon? Well, to put it simply: he doesn't. I'm pretty sure black holes lose their mass over eons, so as the person approaches the event horizon, it will shrink before their eyes, and finally vanish. In essence, falling into the black hole will transport them to the instant of the black hole's annihilation. If he survived the black hole, he will very likely commit suicide shortly afterward, for everyone he ever knew, and all of the human race in addition, will be gone.

Has this conclusion been proposed before?
When we take the Schwarzschild solution and have a test observer falling radially at escape velocity into a black hole he will reach the singularity in finite proper time (e.g. the time on his clock). The remaining time is directly related to the tidal differential and irrespective of the mass (and thus the 'location' of the event horizon).
 

1. What is the event horizon and why is it important?

The event horizon is the boundary surrounding a black hole from which nothing, including light, can escape. It is important because once an object crosses the event horizon, it is impossible for it to escape the gravitational pull of the black hole.

2. Can anything survive passing through the event horizon?

No, according to our current understanding of physics, nothing can survive passing through the event horizon. The immense gravitational force would stretch and compress any object to the point of destruction.

3. Is it possible to escape the event horizon?

No, once an object crosses the event horizon, it is trapped within the black hole. The only way to escape the event horizon would be to travel faster than the speed of light, which is currently considered impossible.

4. Are there any theories or strategies for surviving the event horizon?

There are some theories and strategies proposed by scientists, such as the "firewall" theory which suggests that the event horizon may actually be a fiery barrier that would destroy anything that passes through it. However, these are still just theories and have not been proven.

5. How does time behave near the event horizon?

Time near the event horizon is affected by the immense gravitational force. As an object gets closer to the event horizon, time will appear to slow down, and at the event horizon itself, time would essentially come to a standstill. This is known as time dilation.

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