I You can't actually enter a blackhole?

[blackholesarecool]

TL;DR Summary

If you entered a blackhole, it would decay before you could enter the horizon due to massive time dilation.

You know how people say that nothing can escape a black hole because gravity is faster than light at the event horizon? Well, I’m going to show that, in fact, you can’t even get to the event horizon. Time is slower near a black hole from an outside perspective, but from inside, time actually feels normal. Black holes decay over time, and the decay rate is relative to an outside perspective. For an outside observer, it seems to take forever for an object to reach the horizon. But the black hole decays before that forever time passes, so you never actually cross the event horizon because the black hole is gone by the time you reach it.

The point is that time dilation gives the black hole enough time to decay, relative to an outside observer. The decay happens so quickly from their perspective that, by the time the object would’ve reached the event horizon, the black hole is already gone. So, the event horizon becomes irrelevant—it’s like the black hole evaporates before anything can fall in. This is how the infinite time dilation allows the decay to prevent crossing the horizon, not because time slows down for the object falling in.

 

[Ibix]

It takes forever for an object to enter the horizon of a blackhole

This is a common misconception. It is, at best, only partially true.

You can reach the singularity in finite time (and quite short time at that - microseconds, for a stellar mass black hole).

 

[blackholesarecool]

This is a common misconception. It is, at best, only partially true.

You can reach the singularity in finite time (and quite short time at that - microseconds, for a stellar mass black hole).

i meant to include "from an outside perspective", by now i shouldve editted it

 

[Dale]

i meant to include "from an outside perspective", by now i shouldve editted it

Do you think it is of any comfort to Fred, as he gets pulled apart by tidal forces near the singularity, to think that from Oscar’s perspective he is intact?

I am going to prove

I would be interested in the proof

 

[Ibix]

i meant to include "from an outside perspective", by now i shouldve editted it

Doesn't change anything.

There is an event on an outside observer's worldline where the horizon crossing is no longer in their causal future. That happens at finite time. The infaller is irrevocably inside the black hole at that time. You are now too late to stop it, even in principle - so yes, it's happened.

There is never a Schwarzschild time coordinate simultaneous with the infall event, but that's a failing of Schwarzschild coordinates. They don't cover the horizon. Trying to reason about horizon crossing using them is like trying to determine the compass bearing you need to walk to Mars. It will never get you to a sensible answer.

 

[phyzguy]

i meant to include "from an outside perspective", by now i shouldve editted it

From an outside perspective really isn't what's important , is it? What's important is the perspective of the person falling into the black hole. From your perspective you fall in very quickly, as @Ibix said.

 

[blackholesarecool]

i editted my post, does it clarify a bit more?

 

[Orodruin]

i editted my post, does it clarify a bit more?

No. All it shows is that you don’t really understand black holes.

 

[phinds]

i editted my post, does it clarify a bit more?

No. Your post is based on a misconception. Saying

I’m going to show that, in fact, you can’t even get to the event horizon

continues to show that.

 

[blackholesarecool]

ok then prove that you can make it to the event horizon before the black hole decays and you dont, and before you say, you fall instantly into a blackhole, well, the decay also speeds up, not just time

 

[Orodruin]

ok then prove that you can make it to the event horizon before the black hole decays and you dont, and before you say, you fall instantly into a blackhole, well, the decay also speeds up, not just time

That’s not how things work. You are making the exceptional claim, so you are the one who has to provide proof. Furthermore, the proof you are asking for is available in any introductory textbook on GR.

 

[phinds]

ok then prove that you can make it to the event horizon before the black hole decays and you dont, and before you say, you fall instantly into a blackhole, well, the decay also speeds up, not just time

You continue to spout nonsense. That doesn't go over well here on PF. We deal in actual science, not misconceptions. As @Orodruin suggested, read an introductory textbook on GR and you will understand why we keep telling you you're wrong. As for this thread, quit while you're behind.

 

[blackholesarecool]

could you name some of the misconceptions that i named, so that i dont make these mistakes again

 

[phinds]

could you name some of the misconceptions that i named, so that i dont make these mistakes again

We have already done that. Read the responses.

 

[Ibix]

ok then prove that you can make it to the event horizon before the black hole decays and you dont, and before you say, you fall instantly into a blackhole, well, the decay also speeds up, not just time

Here's a sketch Penrose diagram of an evaporating black hole:

The red line is someone falling in, crossing the event horizon (grey line) into the triangular region representing the hole interior and striking the singularity (wiggly line). The green line is someone not falling into the hole. Note that they get to see (directly observe, e.g. through a telescope) the horizon crossing of the red object at the same time they see the hole evaporate.

 

[blackholesarecool]

which direction is time, if its up ok, but then, where is the decaying though

 

[Ibix]

could you name some of the misconceptions that i named, so that i dont make these mistakes again

You are attaching far too much importance to a more-or-less arbitrary choice of convention for defining simultaneity between events. My analogy with the compass bearing to Mars was not an idle one. The fact that there is no such compass bearing doesn't mean that the trip is impossible. It means that your system of directions doesn't cover the path you need to take. The same is true of picking Schwarzschild-like coordinates (which is what you are doing when you start talking about time dilation) and then trying to think about a horizon crossing. The coordinate system is singular at the horizon so you can't use it to assign a time to events on the horizon using it - but your bad choice of coordinates doesn't limit the physics. There are coordinate systems that are well-behaved at the horizon, and in those there is no problem describing horizon crossing journeys.

 

[Ibix]

which direction is time, if its up ok, but then, where is the decaying though

This diagram is highly distorted. Any direction that is within less than 45° of vertically upwards is something someone can call time.

The evaporation event is the right hand end of the wiggly line - if you imagine extending the event horizon up and to the right, the triangle above that is flat empty spacetime.

 

[Dale]

For an outside observer, it seems to take forever for an object to reach the horizon.

This statement assumes a Schwarzschild spacetime.

the black hole decays before that forever time passes

This statement is false in a Schwarzschild spacetime. I am not completely certain what spacetime describes an evaporating black hole, but it is not a Schwarzschild spacetime.

so you never actually cross the event horizon because the black hole is gone by the time you reach it

This conclusion doesn’t follow because it is based on distinct features of two different spacetimes.

 

[DaveC426913]

Here's a sketch Penrose diagram of an evaporating black hole:

The red line is someone falling in, crossing the event horizon (grey line) into the triangular region representing the hole interior and striking the singularity (wiggly line). The green line is someone not falling into the hole. Note that they get to see (directly observe, e.g. through a telescope) the horizon crossing of the red object at the same time they see the hole evaporate.

Is there a better diagram of this, or can I clean this diagram up?
There's a couple of places I might describe as "the triangular region".
What are the labels?
And I'm still not sure where the time axis is.

 

[PeterDonis]

The point is that time dilation gives the black hole enough time to decay, relative to an outside observer.

No, it doesn't. You need to read this Insights article:

https://www.physicsforums.com/threads/do-black-holes-really-exist-comments.849716/

 

[PeterDonis]

could you name some of the misconceptions that i named, so that i dont make these mistakes again

Read the Insights article I linked to.

 

[PeterDonis]

I am not completely certain what spacetime describes an evaporating black hole

The simplest such model, which is the one Hawking was implicitly using in his original papers, has the Penrose diagram that @Ibix posted in post #15. This model does contain a Schwarzschild region; roughly speaking, if you draw another line going up and to the right at a 45 degree angle a little way below the red horizon line (this marks the boundary of the region occupied by outgoing Hawking radiation), the region to the right of that line and outside the collapsing matter is the Schwarzschild region. In that region, a distant observer (such as the one whose worldline is the green line) will see the collapsing matter approaching the horizon more and more slowly; but before that matter actually reaches the horizon, the observer leaves the Schwarzschild region and enters the region occupied by outgoing Hawking radiation, and from that point on the Schwarzschild model is no longer valid.

 

[Orodruin]

could you name some of the misconceptions that i named, so that i dont make these mistakes again

One of the biggest ones being thinking you can do physics by simply stringing words and popularised descriptions together. You need an actual mathematical model and precise definitions.

You know how people say that

… is not a reliable reference. Please put your argument into an appropriate GR computation.

 

[PeroK]

ok then prove that you can make it to the event horizon before the black hole decays and you dont, and before you say, you fall instantly into a blackhole, well, the decay also speeds up, not just time

The calculation is here, for example:

https://www.physicsforums.com/threads/how-long-does-it-take-to-fall-into-a-black-hole.1000235/

 

[Ibix]

Is there a better diagram of this, or can I clean this diagram up?
There's a couple of places I might describe as "the triangular region".
What are the labels?
And I'm still not sure where the time axis is.

Here's a version without my bad handwriting.

The region I've labelled (a) is the black hole interior, bounded by the singularity (wiggly line) at the top and the event horizon (diagonal line) below. The region (b) is unambiguously before the black hole exists. The region (c) is where and when you can drop stuff into the hole (you can do this from region (b) too, but it has to go via region (c) unless it's exactly on the symmetry axis), but you won't see it fall in yet. Also, you can still argue that the hole hasn't formed yet because it hasn't entered your causal past. In region (d) you've missed your chance to drop anything into the hole, but you still won't have seen anything fall in, and you can say variously that the hole (i) hasn't formed yet; (ii) has formed; (iii) is evaporating at this exact moment; or (iv) has already evaporated. In region (e) the hole has unambiguously evaporated. On the boundary between (d) and (e) is where you see both everything you dropped in crossing the horizon and the hole evaporating.

Broadly, time is up the page. But this is relativity and a highly distorted diagram so there's some flexibility. The key point about these diagrams is that light travels on 45 degree paths. That lets us draw light cones easily. Here are future (red) and past (blue) lightcones for an arbitrary event, the one where the red and blue cones meet.

The "time axis" is any line you draw that stays within 45 degrees of vertical and comes from the point labelled $i^-$ and goes to either the singularity or the corner labelled $i+$. All timelike paths do this if extended far enough back and forward. Lightlike paths begin on the edge labelled $\mathcal{I}^-$ and end on the one labelled $\mathcal{I}^+$. Thing "bounce off" the edge labelled $r=0$, because it's just the origin of polar coordinates and isn't really a boundary.

Not sure if that's made anything clearer.

 

[Dale]

The simplest such model

Sorry, I meant the actual metric. Penrose diagrams are nice, but they don’t give you a metric.

 

[blackholesarecool]

for this

i realized, doesn't the singularity and it evaporating happen at the same time, so you never hit the singularity??

 

[Ibix]

for this
View attachment 357909i realized, doesn't the singularity and it evaporating happen at the same time, so you never hit the singularity??

No. This is relativity, which doesn't have a global notion of "at the same time". What matters is if events are causally connected, and the singularity (or spacelike surfaces approaching the singularity, if we're being careful) is outside the lightcone of the evaporation event. So you can arrive at the singularity whether or not you choose to call this "at the same time as evaporation".

Trying to use your intuition, trained in our every day world, on general relativity will always lead you astray. If you want to reason about this stuff, you need the maths.

 

[Dale]

doesn't the singularity and it evaporating happen at the same time, so you never hit the singularity??

The singularity is spacelike. So you can still hit it if you hit it at a different place than where it evaporates.

 

[PeroK]

TL;DR Summary: If you entered a blackhole, it would decay before you could enter the horizon due to massive time dilation.

You can think of a coordinate system as a map. In GR not every coordinate system includes all of spacetime and all events. The coordinate system you are using, where you have infinite time dilation as you approach the event horizon, is only a partial map of spacetime. There are events that are not shown on that map. I.e. events that have no coordinates in that system. That's a deficiency in your coordianate system. It doesn't mean that those events do not take place.

A very crude analogy is to have a map of only part of the country. Just because towns and cities are not on that map doesn't mean they don't exist. In this analogy, of course, you only have to extend your map - so the deficiency is trivial and can be rectified. In the coordinate system you are using to try to describe a black hole, the coordinate deficiency is subtler and not so easy to rectify. It is nevertheless a deficiency. In particular, you cannot attribute a time for an object falling into a black hole either to crossing the event horizon; or, to running out of time at the singularity.

Instead, if you use a coordinate system that includes these events, then you can attribute a time coordinate to both these events. You can also calculate the proper time elasped for the infalling object (as I have done in the thread referenced above).

One of the problems is that the writers of popular science books and videos love to emphaise this coordinate deficiency and present it as a physical paradox. Whereas, a university textbook on GR would say very much what I've said here and introduce a coordinate system in which a black hole may be studied more fully.

This highlights a key distinction between popular science and university textbooks. The former is designed to interest, excite, entertain and induce a sense of wonder. The latter is intended to explain and provide the student will tools to study problems themselves, without getting caught up in a web of paradoxes.

That's why ultimately you cannot take popular science sources too seriously. And, in particular, you can't use them to argue against the real physics, as taught at university.

 

[DaveC426913]

Not sure if that's made anything clearer.

Thanks. It does. As does scrutinizing the diagram carefully for aas lon as it takes to sort out the directions of space and time and events.

Time essentially passes from past to future from bottom up.
Black hole hole horizon is r=0 (the 2nd one) after it's formed.
Objects Move in space to left (falling in) and right (passing outside) of area a, and in time upward.

 

[PeterDonis]

I meant the actual metric

The metric will be different in the different regions; there won't be a single line element that works for the entire spacetime. Roughly speaking, there is a region where, as I said before, the metric is Schwarzschild; there is the region occupied by the collapsing matter, where the metric in the idealized case of perfectly spherically symmetric collapse is a portion of a closed collapsing FRW metric (as in the 1939 paper by Oppenheimer and Snyder); there is the region occupied by outgoing Hawking radiation, where the metric, again in the idealized case of perfect spherical symmetry, is the outgoing Vaidya metric; and there is the region after the final evaporation of the hole, in which the metric is Minkowski. You then have to impose appropriate junction conditions at the boundaries between these regions.

 

[PeterDonis]

doesn't the singularity and it evaporating happen at the same time

Not in any sense which makes this...

so you never hit the singularity??

...true.

 

[Orodruin]

Time essentially passes from past to future from bottom up.

As has already been hinted at, ”time” is not a single concept in relativity and therefore not in a Penrose diagram. What you do have is the causal structure in that the light cone at each point consists of lines tilted at 45 degrees with the future light-cone being the upper of the resulting areas. In that sense ”time” is ”up” for all observers.

 

[DaveC426913]

As has already been hinted at, ”time” is not a single concept in relativity and therefore not in a Penrose diagram. What you do have is the causal structure in that the light cone at each point consists of lines tilted at 45 degrees with the future light-cone being the upper of the resulting areas. In that sense ”time” is ”up” for all observers.

Yes. That's why I said "essentially". I just meant it for the purpose of broadly reading the diagram.

To those of us who don't frequently examine such diagrams, Ibix' initial diagram can be confusing. It's not even apparent which way the red and green lines are to be interpreted to be moving.

I know this isn't proper, but it at least helps me start to interpret the diagram. Not just the axes, but the arrows on the paths.

 

[PeterDonis]

A separate thread has been spun-off for a more advanced discussion of how the spacetime model of an evaporating black hole works:

https://www.physicsforums.com/threads/spacetime-model-of-evaporating-black-hole.1078883/

 

[DaveC426913]

A separate thread has been spun-off for a more advanced discussion of how the spacetime model of an evaporating black hole works:

https://www.physicsforums.com/threads/spacetime-model-of-evaporating-black-hole.1078883/

And just like that, back to grade school.
"All you guys who finished their four laps slaloming backwards can go over to the main rink and skate with the girls' gym class. You three late bloomers will hang back here on the beginners track using a chair for support - in full view of the rest of your classmates. This won't stunt your social and dating life at all."

_{(Oops. Oversharing?)}

 

[PeterDonis]

This won't stunt your social and dating life at all."

My experience was that the ones in the advanced classes had a lot more trouble getting dates than the ones who weren't.

 

[pervect]

i meant to include "from an outside perspective", by now i shouldve editted it

The outside observer often does not assigns a label (a time coordinate) to the event of someone crossing the event horizon. But that is rather different from saying it doesn't happen. I would suggest instead saying that the outside observer never sees it happen, which will not generate any argument and actually represents the facts. Coordinate charts, the mathematical labels that assign coordinates to events, don't have to cover all of a manifold (such as the Schwarzschild or other type of black hole), they can (and do) often just cover part of the complete manifold.

In addition, while the Schwarzschild coordinates don't assign a label to the event of an infalling observer crossing the event horizon, other coordinates do. For instance, Kruskal coordinates. Thus, you are _assuming_ that your outside observer uses a particular way of viewing things (a particular coordinate chart), making your observation untrue in general without modifications to be more specific.

 

[blackholesarecool]

oh i think i realized it now, time doesnt actually slow, its because it looks like it does, ok now i think i get it better