I You can't actually enter a blackhole?

[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