Black holes and evaporation

[md65536]

3 hours ago, Mordred said:

So how one defines the light one also involves the coordinate choice.

Are you saying that you get different light cones with different coordinate choices? But if you have light from one event reaching another event on its future light cone, that doesn't change depending on coordinates, so I don't know what you mean.

4 hours ago, Mordred said:

Also there is a significant difference from what an observer at rest will note and an infalling observer. They will have significantly different lightcones.

This makes no sense to me. Isn't it the events that have light cones, not observers? For example, if you have an event where an infalling observer contacts a hovering observer as it passes, that event has a light cone. Are you saying it has different light cones for the different observers?

[Mordred]

I will have to crunch some mathematics involving the Schwartzchild metric to demonstrate for the infalling as opposed to at rest observer.

However you should recognize the Schwartzchild singularity is a coordinate singularity as per

https://en.m.wikipedia.org/wiki/Eddington–Finkelstein_coordinates

An infalling observer is undergoing rapidity (acceleration) also your dealing with curved spacetime so it will take me a bit to latex the examples. I should have time tonight for that.

[Markus Hanke]

On 6/16/2020 at 5:17 PM, rjbeery said:

My issue is that this, and almost any, definition makes finite black holes a logical impossibility. In other words, any process (e.g. Hawking radiation, which I generically refer to as "evaporation"') that eventually eliminates the event horizon has, by the definition of black holes, negated that black hole's existence for all time, including the past. Evaporation and event horizons are mutually exclusive ideas.

Just because some event isn’t in some arbitrary observer’s past light cone does not mean that this event does not exist. I don’t understand how you arrived at that conclusion...? Any pair of events the spacetime interval between which is space-like are not causally connected, yet that does not say anything about their existence.
Furthermore, the Hawking temperature of a Schwarzschild black hole is a function of event horizon surface area (without a horizon there is no entropy), so evaporation requires an event horizon. And since Hawking radiation itself propagates outward at finite speed - like any other type of radiation -, it would still be detectable by distant observers after the evaporation process has ended in the black hole’s rest frame, giving a clear indication that the black hole has indeed existed.

21 hours ago, rjbeery said:

my feeling is that this "island" is no longer on a differentiable manifold when it becomes disconnected from the traditional future null infinity (the infinite future according to us).

At what point(s) other than the singularity do you think it is not differentiable?

[rjbeery]

5 minutes ago, Markus Hanke said:

Just because some event isn’t in some arbitrary observer’s past light cone does not mean that this event does not exist.

Agreed, but I'm talking about a specific observer who is located at a point in space which "used to" contain a black hole. The black hole resides in the past of this observer. If you can't see the contradiction here, please refer to the diagram.

[Markus Hanke]

On 6/16/2020 at 5:17 PM, rjbeery said:

This clearly puts the entire history of this MBH in our causal past, and CERTAINLY in the causal past of future null infinity. That region in spacetime of our lab containing this theoretical MBH cannot have included an event horizon.

Again, I do not understand your reasoning. This is a non-sequitur, because none of the events below the event horizon are in our causal past. Everything your instrument has recorded over night has originated at or above the event horizon, without exception - and the existence of events above the horizon does not imply that events below the horizon must have been in our causal past too. The opposite, in fact - it excludes the possibility.

2 minutes ago, rjbeery said:

Agreed, but I'm talking about a specific observer who is located at a point in space which "used to" contain a black hole. The black hole resides in the past of this observer.

Only the exterior region above the horizon does - the interior region has no time-like nor light-like causal connection to the observer. There is no future-oriented geodesic that would take a test particle back out from below the horizon, but that does not imply that the test particle can’t exist.

[rjbeery]

11 minutes ago, Markus Hanke said:

Only the exterior region above the horizon does - the interior region has no time-like nor light-like causal connection to the observer. There is no future-oriented geodesic that would take a test particle back out from below the horizon, but that does not imply that the test particle can’t exist.

Some of these comments are presuming the existence of the event horizon, first, and then leaning on the definition of them as a defending explanation of them. Please refer to the diagram to see my objection. The formation of event horizons takes an infinite amount of coordinate time. We can map this using Penrose diagrams, where the top of the customary diagram represents the "infinite future". When we attempt to use a Penrose diagram to illustrate events after an event horizon has formed, we are now showing spacetime coordinates (events) which have already occurred, and have been accounted for. (r=0, t=100) is represented twice in the diagram, for example.

[md65536]

2 hours ago, Mordred said:

An infalling observer is undergoing rapidity (acceleration) 

You keep referring to rapidity as acceleration. The only definitions I've seen are that it's a measure of relativistic velocity. What definition are you using? Your statement makes as little sense as saying an infalling observer is undergoing velocity.

[Mordred]

6 minutes ago, md65536 said:

You keep referring to rapidity as acceleration. The only definitions I've seen are that it's a measure of relativistic velocity. What definition are you using? Your statement makes as little sense as saying an infalling observer is undergoing velocity.

No rapidity is a term used to describe the hyperbolic rotations due to Lorentz boosts. It is not involved under constant velocity.

[md65536]

8 minutes ago, Mordred said:

No rapidity is a term used to describe the hyperbolic rotations due to Lorentz boosts. It is not involved under constant velocity.

??? From https://en.wikipedia.org/wiki/Lorentz_transformation : "Transformations describing relative motion with constant (uniform) velocity and without rotation of the space coordinate axes are called boosts, and the relative velocity between the frames is the parameter of the transformation." Do you think a boost is an acceleration? Can you please provide references to the definitions you're using (including rapidity)? I don't trust what you're saying because it's not making any sense to me with respect to anything else I read.

[Mordred]

Look at the formulas do you require trigonometric functions for constant velocity ? There are six types of boosts and three rotations. 

https://en.m.wikipedia.org/wiki/Lorentz_transformation

The example they give here is a rotation in spacetime which is a form of acceleration.

[paulsutton]

On 6/16/2020 at 2:25 AM, rjbeery said:

Understood. The following is from page 3 of the LHC Safety Assessment Group report which was made prior to the Large Hadron Collider's construction.

I assume we can all agree that this paper has been sufficiently vetted and generally reflects a consensus of the physics community regarding black holes, micro black holes, Hawking radiation and the "basic physical principles" on which those objects are predicted.

I'm just trying to nail down exactly what we're talking about before I relay my issue with black holes, because in my experience people can get a bit "hand-wavy" on the subject.

 

This is great. So if a space contains no event horizon then we will agree that it does not contain a black hole?

But can't other objects warp space - time and therefore would the edge of that warp be an event horizon ?  Not sure if supermassive stars have an effect on the surrounding space.

I am no where near an expert, so asking this more as a speculative question.

 

[md65536]

23 minutes ago, Mordred said:

Look at the formulas do you require trigonometric functions for constant velocity ?

Sure, if you're using hyperbolic functions with the Lorentz transformation. Not relevant here.

32 minutes ago, Mordred said:

The example they give here is a rotation in spacetime which is a form of acceleration.

It isn't. Have you actually read your link? You should.

None of these terms are relevant to this thread. They're worse than irrelevant when used incorrectly.

[Mordred]

Sigh your still not getting it.

Here there is a clear example of the acceleration aspects and rapidity under the twin paradox

https://www.google.com/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1701.02731&ved=2ahUKEwi9lqfzj4zqAhVCoFsKHRaXCHIQFjAFegQIAhAM&usg=AOvVaw3vAZGh65NWKJZiFukMfOZ0

Though a better example is under Introductory to GR by Lewis Ryder.

Edited June 18, 2020 by Mordred

[Halc]

5 hours ago, rjbeery said:

I'm talking about a specific observer who is located at a point in space which "used to" contain a black hole. The black hole resides in the past of this observer. If you can't see the contradiction here, please refer to the diagram.

In the coordinate space defined by such an observer, the black hole doesn't exist and never (yet) existed.  Any object tossed in (from the perspective of this specific observer) was still outside the event horizon, even a moment before the evaporation completes.  There is no line of simultaneity reaching from any point on this observers worldline into the black hole. Said hyperplane of simultaneity always remains unbroken (no hole in it), clean to the other side. It's as if all events comprising that region of spacetime exist only entirely in the future of this observer, even when the black hole is evaporated.

Edited June 18, 2020 by Halc

[rjbeery]

2 minutes ago, Halc said:

In the coordinate space defined by such an observer, the black hole doesn't exist and never (yet) existed.  Any object tossed in (from the perspective of this specific observer) was still outside the event horizon, even a moment before the evaporation completes.  There is no line of simultaneity reaching from any point on this observers worldline into the black hole. Said hyperplane of simultaneity always remains unbroken (no hole in it), clean to the other side. It's as if all events comprising that region of spacetime exist only entirely in the future of this observer, even when the black hole is evaporated.

Then you agree that an observer residing in the upper part of Hawking's diagram (after the evaporation) has a coordinate time less than the time represented by any point residing at r=0 between the event horizon and the singularity below it on the graph?

[Halc]

13 minutes ago, rjbeery said:

Then you agree that an observer residing in the upper part of Hawking's diagram (after the evaporation) has a coordinate time less than the time represented by any point residing at r=0 between the event horizon and the singularity below it on the graph?

No, I do not. It is not meaningful to compare the time of an event to an event not in your coordinate space.  Use different coordinates if you want to do this.

[rjbeery]

1 minute ago, Halc said:

No, I do not. It is not meaningful to compare the time of an event to an event not in your coordinate space.  Use different coordinates if you want to do this.

Wait a minute. That is literally the purpose of Penrose diagrams -- to follow causality through and beyond the event horizon. To say "it isn't meaningful" is the same thing as proclaiming that Penrose diagrams aren't meaningful.

[md65536]

32 minutes ago, Halc said:

In the coordinate space defined by such an observer, the black hole doesn't exist and never (yet) existed.

I don't think that's correct. It did exist, and it evaporated in the observer's past. It's only the interior events that aren't causally connected to the observer in the moment described.

2 hours ago, Mordred said:

Sigh your still not getting it.

Here there is a clear example of the acceleration aspects and rapidity under the twin paradox

https://www.google.com/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1701.02731&ved=2ahUKEwi9lqfzj4zqAhVCoFsKHRaXCHIQFjAFegQIAhAM&usg=AOvVaw3vAZGh65NWKJZiFukMfOZ0

How is this relevant to the thread? Your link confirms that rapidity is not acceleration. Quote: "rapidity η (v) ≡ tanh^−1 (v)". Constant rapidity implies constant velocity. Do you understand that rapidity is not acceleration? See https://en.wikipedia.org/wiki/Rapidity :

Quote

In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates.

For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional, but for higher velocities, rapidity takes a larger value, the rapidity of light being infinite.

If you still think rapidity is acceleration or requires acceleration or whatever, can you please provide a definition that you're using?

[Halc]

16 minutes ago, rjbeery said:

Wait a minute. That is literally the purpose of Penrose diagrams -- to follow causality through and beyond the event horizon. To say "it isn't meaningful" is the same thing as proclaiming that Penrose diagrams aren't meaningful.

I never said any particular coordinate system wasn't meaningful. It isn't meaningful to compare the times of the two events you indicate.

The Penrose diagram demonstrates the same thing in this case.  An event within the black hole (an event that doesn't exist in the coordinate space discussed in my prior post, but does exist in the Penrose diagram) has no causal connection with the event after the evaporation.  That makes it like any pair of events separated in a space-like manner: There is no objective comparison of their times.  A-before-B is a relation dependent on the foliation of choice, because neither event is in the past or future light cone of the other.

Edited June 18, 2020 by Halc

[rjbeery]

1 hour ago, Halc said:

I never said any particular coordinate system wasn't meaningful. It isn't meaningful to compare the times of the two events you indicate.

The Penrose diagram demonstrates the same thing in this case.  An event within the black hole (an event that doesn't exist in the coordinate space discussed in my prior post, but does exist in the Penrose diagram) has no causal connection with the event after the evaporation.  That makes it like any pair of events separated in a space-like manner: There is no objective comparison of their times.  A-before-B is a relation dependent on the foliation of choice, because neither event is in the past or future light cone of the other.

I'm not bothered by the notion of "no causal connection" but you cannot say that an event within the black hole "doesn't exist in the coordinate space". That's nonsensical. The entire point of this coordinate system is to give unique, well-ordered labels to events in spacetime.

Edited June 19, 2020 by rjbeery

[Mordred]

Ok this is bordering on getting off topic but consider two observers.

One a rest watching an infalling object. That observer will never see the object cross the EH.

Now in the infalling objects case that observer will cross the EH in a finite time period. Is the end no that observer will see future events that the observer at rest will not experience.

Here is a relevant paper. Title is 

" Is it possible to see the infinite future of the universe when falling into a Black hole "

http://arxiv.org/pdf/0906.1442v1.pdf

Now note that this paper also describes a coordinate choice that can applied beyond the EH. 

 Different coordinate systems can give different results. 

The EH is a coordinate singularity it is not a true singularity I already supplied a reference for that statement.

Now given the last paper can you state the two observers experience identical causal connections  ?

Can you state an observer in the interior of the EH is causally disconnected from the universe outside the EH ? I will supply the coordinate system that describes this region.

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

Just to give you better details on the Coordinate singularity and how to remove the singularity see

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap12.pdf&ved=2ahUKEwirjPaQ5YzqAhUJop4KHRgHCrQQFjALegQIAxAI&usg=AOvVaw3mu5haWWZXIJt3HKgb-vMS

 

 

Edited June 19, 2020 by Mordred

[Halc]

19 minutes ago, Mordred said:

Is the end no that observer will see future events that the observer at rest will not experience.

Here is a relevant paper. Title is 

" Is it possible to see the infinite future of the universe when falling into a Black hole "

http://arxiv.org/pdf/0906.1442v1.pdf

Now note that this paper also describes a coordinate choice that can applied beyond the EH. 

 Different coordinate systems can give different results. 

I've seen it demonstrated with a Kruskal-Szekeres diagram that an infalling observer can only witness a finite future as measured by an outside observer.  He cannot see the universe end.

[Mordred]

Yes in that particular coordinate choice. However in the Schwartzchild metric itself you can get different results. The paper above described the differences. Though I am positive there are more current examinations.

 I would also not be surprised at different results within the same coordinate choice between authors. It's been a contented item for a number of years.

Edited June 19, 2020 by Mordred

[md65536]

22 minutes ago, Mordred said:

Now given the last paper can you state the two observers experience identical causal connections  ?

Can you state an observer in the interior of the EH is causally disconnected from the universe outside the EH ? I will supply the coordinate system that describes this region.

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

 

Exploring the causal connections with black holes seems related enough to the topic.

I'd say that causal connections are invariant. I think light cones are invariant. A light signal from one event either reaches (causes) another event, or it doesn't. That doesn't change depending on observer. I don't know what you mean by "experience" but of course different observers will see things appear differently, observe different parts of spacetime etc.

Obviously if a particle can survive (as expected) falling into a BH, there can be causal connections from outside to in. As far as I know, it is not known exactly what an observer inside the black hole would observe, as that requires some speculative extrapolation of testable physics. It is only causal connections from inside to out that are prohibited.

[Mordred]

Agreed but let's ask a question. Where is the null surface located ? Under one coordinate choice its r_s= 2GM. However this isn't true for the Kruskal.

Now ask yourself is it the spacelike or the time like that are invariant under the Lorentz transforms ? 

This question becomes important to understand the region's of the Penrose diagrams.

Here is an examination of different causal connections in different coordinate systems the article is specifically dealing with Penrose diagrams.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://people.uncw.edu/hermanr/GRcosmo/penrose.pdf&ved=2ahUKEwixr5mr7IzqAhWHvZ4KHZhcA44QFjAAegQIARAB&usg=AOvVaw0E2LE-32F7TxpcK6vXujWN

Edited June 19, 2020 by Mordred