Black holes and evaporation

[rjbeery]

I have some problems/questions regarding the existence of black holes. First, here is the current state-of-affairs in the physics community AFAIK:

1. Black holes "exist" in the sense that they are physical objects in the Universe
2. Black holes contain an event horizon, located at the Schwarzschild radius, beyond which "nothing can escape"
3. Black holes are likely located at the center of many galaxies, including our own; "micro black holes" are also likely formed and quickly evaporate in our atmosphere due to relativistic cosmic rays
4. Quantum mechanics is anticipated to resolve any mathematical singularity issues at the center of black holes
5. There are a variety of theories, most notably Hawking Radiation, that predict an "evaporation" of black holes over extraordinarily long periods of time

Does anyone feel this any of these statements are inaccurate?

[Strange]

They all seem accurate except:

1 hour ago, rjbeery said:

"micro black holes" are also likely formed and quickly evaporate in our atmosphere due to relativistic cosmic rays

I don't think there is any evidence that this happens, even though it is a theoretical possibility.

 

And, rather than "black holes contain an event horizon" I would say "black holes are an event horizon." But that's just a choice of words.

[rjbeery]

2 hours ago, Strange said:

I don't think there is any evidence that this happens, even though it is a theoretical possibility.

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.

Quote

We focus our attention mainly on two phenomena of current interest, namely the possible production of microscopic black holes, such as might appear in certain theoretical models featuring additional dimensions of space, and the possible production of ‘strangelets', hypothetical pieces of matter analogous to conventional nuclei, but containing also many of the heavier strange quarks. These were both considered carefully in the 2003 report of the LHC Safety Study Group [1]....

...In the case of microscopic black holes, there has been much theoretical speculation since 2003 about their existence and their possible experimental signatures, as reviewed in [2], where references may be found....

...In the case of the hypothetical microscopic black holes, as we discuss in Section 4, if they can be produced in the collisions of elementary particles, they must also be able to decay back into them. Theoretically, it is expected that microscopic black holes would indeed decay via Hawking radiation, which is based on basic physical principles on which there is general consensus. If, nevertheless, some hypothetical microscopic black holes should be stable, we review arguments showing that they would be unable to accrete matter in a manner dangerous for the Earth [2]. If some microscopic black holes were produced by the LHC, they would also have been produced by cosmic rays and have stopped in the Earth or some other astronomical body, and the stability of these astronomical bodies means that they cannot be dangerous

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.

 

2 hours ago, Strange said:

And, rather than "black holes contain an event horizon" I would say "black holes are an event horizon." But that's just a choice of words.

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

[Mordred]

Correct on both accounts. No microblackholes formed at the LHC other other particle accelerators.

 Also a BH must have an event horizon.

[Endy0816]

4 hours ago, rjbeery said:

I have some problems/questions regarding the existence of black holes. First, here is the current state-of-affairs in the physics community AFAIK:

1. Black holes "exist" in the sense that they are physical objects in the Universe
2. Black holes contain an event horizon, located at the Schwarzschild radius, beyond which "nothing can escape"
3. Black holes are likely located at the center of many galaxies, including our own; "micro black holes" are also likely formed and quickly evaporate in our atmosphere due to relativistic cosmic rays
4. Quantum mechanics is anticipated to resolve any mathematical singularity issues at the center of black holes
5. There are a variety of theories, most notably Hawking Radiation, that predict an "evaporation" of black holes over extraordinarily long periods of time

Does anyone feel this any of these statements are inaccurate?

The last is potentially inaccurate.

Only fairly large ones take long periods of time.

Edited June 16, 2020 by Endy0816

[MigL]

Any BH which is not the result of stellar gravitational collapse can be termed a microBH, even quantum BHs could be formed at energies in the TeV range. as was 'feared' at the LHC.
None were observed, as expected, since cosmic rays reach energies of hundreds of TeVs, yet do no damage at all.
Micro BHs that are small enough would be vigorous emitters of Hawking radiation, as their 'temperature'  would be extremely high. As such they would evaporate rather quickly, and be extremely easy to spot.
None have ever been observed, possibly indicating that comparatively large micro BHs did not form in the hot, dense primordial universe as it was too isotropic and homogeneous, while quantum BHs may need much higher energies to form, or may not be possible.
One could assume BHs can form at any mass above the Planck mass , however...

 "All this assumes that the theory of general relativity remains valid at these small distances. If it does not, then other, presently unknown, effects might limit the minimum size of a black hole. Elementary particles are equipped with a quantum-mechanical, intrinsic angular momentum (spin). The correct conservation law for the total (orbital plus spin) angular momentum of matter in curved spacetime requires that spacetime is equipped with torsion. The simplest and most natural theory of gravity with torsion is the Einstein–Cartan theory.^[7][8] Torsion modifies the Dirac equation in the presence of the gravitational field and causes fermion particles to be spatially extended. In this case the spatial extension of fermions limits the minimum mass of a black hole to be on the order of 10¹⁶ kg, showing that micro black holes may not exist. The energy necessary to produce such a black hole is 39 orders of magnitude greater than the energies available at the Large Hadron Collider, indicating that the LHC cannot produce mini black holes. But if black holes are produced, then the theory of general relativity is proven wrong and does not exist at these small distances. The rules of general relativity would be broken, as is consistent with theories of how matter, space, and time break down around the event horizon of a black hole. This would prove the spatial extensions of the fermion limits to be incorrect as well. The fermion limits assume a minimum mass needed to sustain a black hole, as opposed to the opposite, the minimum mass needed to start a black hole, which in theory is achievable in the LHC under some conditions.^[9][10]"

From      https://en.wikipedia.org/wiki/Micro_black_hole

As to whether you can have a BH without an event horizon, the Kerr metric describing space-time around a rotating, non-charged symmetric BH, postulates the dissolution of the non-spherical event horizon when certain rotation conditions are met, allowing for a 'naked singularity'.
The Kerr metric is an exact solution, but as with the Schwarzschild and Reissner-Nordstrom metrics, it may not be a physical solution.

[Strange]

6 hours ago, rjbeery said:

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

Note that the description is entirely hypothetical and condition:  "If some microscopic black holes were produced by the LHC, they would also have been produced by cosmic rays"

The report was written to reassure people that there was no danger from the LHC: the conclusion was that there was no evidence that such microscopic black holes could be created. If they could be created they would decay. And even if they could be created, they can't be dangerous because cosmic rays would produce more of them than the LHC could. But they are hypothetical with no reason to think they exist.

6 hours ago, rjbeery said:

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

Yes, it is the event horizon that defines a black hole.

4 hours ago, MigL said:

As to whether you can have a BH without an event horizon, the Kerr metric describing space-time around a rotating, non-charged symmetric BH, postulates the dissolution of the non-spherical event horizon when certain rotation conditions are met, allowing for a 'naked singularity'.
The Kerr metric is an exact solution, but as with the Schwarzschild and Reissner-Nordstrom metrics, it may not be a physical solution.

Then I guess the question is whether the is really a black hole. With no event horizon, the singularity would be visible meaning that light can travel all the way from the singularity to the external observer. Hence not "black" (nor even a hole!)

 

Maybe worth adding that, as singularities have been brought up, they probably do not represent something physical but show that the current theory is unable to describe what happens.

[joigus]

4 hours ago, MigL said:

Any BH which is not the result of stellar gravitational collapse can be termed a microBH, even quantum BHs could be formed at energies in the TeV range. as was 'feared' at the LHC.[...]

Nice summary. +1.

[rjbeery]

One of the more common definitions of black holes is a variation on

Quote

An asymptotically flat [and strongly asymptotically predictable] spacetime M is said to contain a black hole if not every point of M is contained in the causal past of future null infinity.

The black hole region, B, of such a spacetime is defined to be the points of M not contained in the causal past of future null infinity. The boundary of B in M is called the event horizon.

The above is pulled from here and is credited to Robert Wald.

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.

To make this point clear, imagine the hypothetical micro black holes (MBH) forming in our atmosphere due to cosmic rays. They form, let's say in our physics lab on some random night, and almost immediately decay (as declared by the authors of the LHC Safety Assessment Group paper):

Quote

...if they can be produced in the collisions of elementary particles, they must also be able to decay back into them...

We come back the next morning and have equipment that recorded the MBH's existence. We can also verify that the MBH no longer exists. 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.

This, of course, applies to black holes of any size and any arbitrarily long, but finite, evaporation time. We can always travel to the region in space where the black hole "used to exist" and declare that region to be completely within our past light cones, contradicting the notion that an event horizon ever existed there in the first place.

[Halc]

Edit doesn't work and all the quotes were nullified, so posting this again.

Robert Wald:  An asymptotically flat [and strongly asymptotically predictable] spacetime M is said to contain a black hole if not every point of M is contained in the causal past of future null infinity. The black hole region, B, of such a spacetime is defined to be the points of M not contained in the causal past of future null infinity. The boundary of B in M is called the event horizon.

rjbeery:  My issue is that this, and almost any, definition makes finite black holes a logical impossibility.

I don't find it a logical impossibility.  The definition puts us in a black hole actually, since any location in space beyond the visible universe at t=infinity (currently a location about 65 BLY away) is not in our future light cone, nor are we in its past light cone.

As for the more classic black hole, yes, any event within it is not containied within the causal past of an event near where the black hole completed its evaporation yesterday. That makes it existing by that definition, not a logical impossibility at all. 

rjbeery: 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.

For these to be mutually exclusive, I think you need to make some additional premises which are simply not axiomatic.  For one, my personal destruction (death say) does not negate my existence for all time, I still exist in 2020. So not sure what you mean by those words.  Sure, it doesn't exist at that future time, but that future time is not 'all time', despite your assertion otherwise.  Perhaps if you state the contradiction formally.

rjbeery:  We come back the next morning and have equipment that recorded the MBH's existence. We can also verify that the MBH no longer exists. This clearly puts the entire history of this MBH in our causal past

It does not put the interior events in our causal past, so this is not clear at all.

 

The mathematics can be used to explore whether or not any of the events (I hate calling them points) of M inside said event horizon are in fact contained in the causal future of events outside the event horizon.  It is after all just a mathematical singularity.  A rock fall through a Rindler horizon (another mathematical singularity, not a physical one) effortlessly and without notice by the rock. But it is arguable that a similar rock cannot be dropped into a black hole, instead forming a dense timeless shell. I'm having a hard time finding links on this interpretation.

Edited June 16, 2020 by Halc

[rjbeery]

13 minutes ago, Halc said:

The definition puts us in a black hole actually, since any location in space beyond the visible universe at t=infinity (currently a location about 65 BLY away) is not in our future light cone, nor are we in its past light cone.

From our perspective, the points beyond the visible universe are within the "black hole" that you're referring to, which is fine. That definition would be broken if we could somehow reach those locations at some point in the future, which we cannot (unless cosmic expansion reverses at some point?)

That's the exact problem with "local" black holes. We can literally travel to the location of their existence and wait for them to evaporate. That entire region is now wholly within our past light cone. GR demands that spacetime is a differentiable manifold so we can't simply proclaim that this "remote island of spacetime" exists in our past but somehow has eluded existing in our causal past.

22 minutes ago, Halc said:

It does not put the interior events in our causal past, so this is not clear at all.

It does put them in our past. The earliest reference to this concept that I can find is in Hawking's paper. Below is the graphic used, and a visualization of the problem (in green).

[MigL]

These 'impossibilities' that we naively label Black Holes fully account for stellar motions within the central region of our galaxy ( and others ).
These 'impossibilities' emit copious amounts of radiation from their accretion discs.
And there are many pictures on the internet of one of these 'impossibilities' that was imaged last year.

Don't confuse definitions, or the model, with reality.
GR is extremely accurate, but has a number of failings with regard to BHs.

[rjbeery]

2 hours ago, MigL said:

These 'impossibilities' that we naively label Black Holes fully account for stellar motions within the central region of our galaxy ( and others ).
These 'impossibilities' emit copious amounts of radiation from their accretion discs.
And there are many pictures on the internet of one of these 'impossibilities' that was imaged last year.

Don't confuse definitions, or the model, with reality.
GR is extremely accurate, but has a number of failings with regard to BHs.

GR's treatment of gravity already accounts for stellar motions and accretion discs without requiring event horizons. It's entirely possible that black holes exist, but then it's also possible that the center of galaxies are full of unicorns and lemon ice cream. If GR has "a number of failings with regard to BHs" then you have no model whatsoever to predict them.

[md65536]

8 hours ago, rjbeery said:

We come back the next morning and have equipment that recorded the MBH's existence. We can also verify that the MBH no longer exists. 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.

The definition you quoted, "The black hole region, B, of such a spacetime is defined to be the points of M not contained in the causal past of future null infinity." If there was a black hole then there were such points, which means there must be an event horizon. There's no contradiction there.

Can you give an example of an event from inside the theoretical MBH's horizon that causes an effect outside, such that it has some recorded effect "in the lab the next morning"? If so, then you're on to something. If not, you're making extraordinary claims without evidence.

8 hours ago, rjbeery said:

We can always travel to the region in space where the black hole "used to exist" and declare that region to be completely within our past light cones, contradicting the notion that an event horizon ever existed there in the first place.

It's events that are in past light cones, not spatial regions. Assuming you know that, you mean something like that all the events at that location in a given Euclidean coordinate system, but with earlier times, are in our event's past light cone. However, the events within the past black hole's event horizon are not part of that Euclidean coordinate system, I think. If you were claiming that black hole event horizons can't exist in a Euclidean spacetime, I think you'd be right.

[Endy0816]

2 hours ago, rjbeery said:

GR's treatment of gravity already accounts for stellar motions and accretion discs without requiring event horizons. It's entirely possible that black holes exist, but then it's also possible that the center of galaxies are full of unicorns and lemon ice cream. If GR has "a number of failings with regard to BHs" then you have no model whatsoever to predict them.

No. We know something has to occur due to the finite speed of light when density crosses the critical threshold.

Other thing is nothing else can match a BH for compactness. Accretion disk of an equally massive star still can't orbit as closely.

Whatever goes in is lost. Outside we never learn what has happened, if anything, past the Event horizon.

Edited June 17, 2020 by Endy0816

[Strange]

15 hours ago, rjbeery said:

One of the more common definitions of black holes is a variation on

The above is pulled from here and is credited to Robert Wald.

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.

To make this point clear, imagine the hypothetical micro black holes (MBH) forming in our atmosphere due to cosmic rays. They form, let's say in our physics lab on some random night, and almost immediately decay (as declared by the authors of the LHC Safety Assessment Group paper):

We come back the next morning and have equipment that recorded the MBH's existence. We can also verify that the MBH no longer exists. 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.

This, of course, applies to black holes of any size and any arbitrarily long, but finite, evaporation time. We can always travel to the region in space where the black hole "used to exist" and declare that region to be completely within our past light cones, contradicting the notion that an event horizon ever existed there in the first place.

I don't fully understand the argument you are making. But I think the key point is that it is the inside of the black hole that is not causally connected to the outside.  It is not the event horizon or even the (past) existence of the black hole.

In the case of an evaporating black hole, any photon inside the black hole before evaporation will not escape before the black hole evaporates. It will reach the singularity and disappear before the collapsing event horizon could reach it and allow it to escape.

(This assumes that black holes can evaporate completely, which is no clear but might be off topic.)

13 hours ago, rjbeery said:

rom our perspective, the points beyond the visible universe are within the "black hole" that you're referring to, which is fine. That definition would be broken if we could somehow reach those locations at some point in the future, which we cannot (unless cosmic expansion reverses at some point?)

It is not reaching those locations that is the issue (there are problems with defining what "reaching that location" means, but that doesn't matter for the moment.

It is an event horizon not a location horizon.

An "event" is position in 4D space-time coordinates. So by the time the event horizon evaporates, that "event" is no longer accessible (it is in your past). 

One you pass beyond the event horizon, then every direction towards the "outside" is in your past and every direction towards the singularity is your future. That is why there is no escape, and no causal communication outwards.

Edit: I see md65536 made the same point more succinctly.

7 hours ago, rjbeery said:

GR's treatment of gravity already accounts for stellar motions and accretion discs without requiring event horizons.

If you are happy to use GR to explain the orbits of the stars around a compact massive body at Sagittarius A* then you can't refuse to use GR when it predicts an event horizon. Picking which bits of a theory you use because you don't like the results is just not rational.

7 hours ago, rjbeery said:

It's entirely possible that black holes exist, but then it's also possible that the center of galaxies are full of unicorns and lemon ice cream. If GR has "a number of failings with regard to BHs" then you have no model whatsoever to predict them.

The "we don't know everything therefore we don't know anything" is weak at the best of times. It fails spectacularly when there is a lot of direct evidence for the existence of black holes.

Edited June 17, 2020 by Strange

[swansont]

11 hours ago, rjbeery said:

GR's treatment of gravity already accounts for stellar motions and accretion discs without requiring event horizons. It's entirely possible that black holes exist, but then it's also possible that the center of galaxies are full of unicorns and lemon ice cream. If GR has "a number of failings with regard to BHs" then you have no model whatsoever to predict them.

GR doesn't fail to predict them, as they are a prediction of GR. That's not where the failure is.

[rjbeery]

8 hours ago, Strange said:

An "event" is position in 4D space-time coordinates. So by the time the event horizon evaporates, that "event" is no longer accessible (it is in your past). 

Being in my past is exactly the problem. It's directly contradicts the descriptive definition of event horizons and black holes.

3 hours ago, swansont said:

GR doesn't fail to predict them, as they are a prediction of GR. That's not where the failure is.

The problem isn't GR; it's GR + some process that makes black holes finite (in this case, evaporation). Event horizons and finite black holes are mutually incompatible, and since we agree that black holes require an event horizon then the very term "finite black hole" is an oxymoron.

 

[Strange]

19 minutes ago, rjbeery said:

Being in my past is exactly the problem. It's directly contradicts the descriptive definition of event horizons and black holes.

No it doesn't. It would only contradict it if something from that event could affect you. For example, if a photon were released at that time and space; you would never be able to detect it because it could never leave the the black hole. Even if the black hole evaporates. So when I said it was in your past, I did not mean it is in you past light cone. (I probably should not have said that, it is misleading and arguably wrong.)

22 minutes ago, rjbeery said:

The problem isn't GR; it's GR + some process that makes black holes finite (in this case, evaporation). Event horizons and finite black holes are mutually incompatible, and since we agree that black holes require an event horizon then the very term "finite black hole" is an oxymoron.

They are only incompatible with your understanding of what an event horizon means.

In the case of an evaporating black hole, any photon that happens to  inside the black hole before evaporation cannot escape before the black hole evaporates. It will reach the singularity and disappear before the collapsing event horizon could reach it and allow it to escape. Changes to the event horizon are limited to occur at the speed of light. A photon inside the event horizon is heading towards the singularity at the speed of light. So the event horizon can never "overtake" the photon and leave it outside the event horizon.

 

However, more generally, there may be some truth to what you say. We don't yet know what effect adding quantum theory to GR will have on our understanding of the event horizon. Hawking did some work that suggested the event horizon may be less well defined, possibly porous (from my limited understanding of the work). There also things like the firewall paradox, that show we don't yet know the full story. But none of that is enough to assert "event horizons don't exist" when the evidence (including a photograph of the accused) implies they do.

[md65536]

2 hours ago, rjbeery said:

Being in my past is exactly the problem. It's directly contradicts the descriptive definition of event horizons and black holes.

Is it fair to say your argument is basically, "if a black hole's entire existence is within an event's past light cone, then any interior events of the black hole are also within that event's past light cone"?

I think the argument is false. The interior events are not in your past light cone. For one thing, a light cone is based on the paths of light from one event to another, and a black hole doesn't have such paths from interior events to exterior.

I think what you're doing is using a mathematical definition of a light cone in "Your" flat spacetime. Then with a black hole placed in that past light cone, you're effectively assigning flat spacetime coordinates to events within the black hole, like you might do if the black hole wasn't there at all and the spacetime remained flat. You're effectively giving physically meaningless flat-spacetime coordinates to events in a curved spacetime, which I think is okay, but then you're drawing conclusions about those events based on physics that applies in flat spacetimes, which is not correct. In the curved spacetime, the black hole's interior events are geometrically outside of your past light cone, I think... or, I have no idea.

Maybe another way to put it is that black holes tilt light cones, and you're not accounting for that.

As an amateur, I think I'm missing the maths and vocab that would make this clear and precise.

 

edit: Thinking more about tilted light cones... Say the event of the BH evaporating is in your past light cone. You can say there's a causal connection between you and it because its future light cone intersects your past light cone. But for an event within the BH's horizon, the event's future light cone is tilted more than 45 degrees such that its future light cone does not intersect your past light cone, and there is no causal connection. I suspect there's more to it than that.

Edited June 17, 2020 by md65536

[rjbeery]

1 hour ago, Strange said:

No it doesn't. It would only contradict it if something from that event could affect you. For example, if a photon were released at that time and space; you would never be able to detect it because it could never leave the the black hole. Even if the black hole evaporates. So when I said it was in your past, I did not mean it is in you past light cone.

26 minutes ago, md65536 said:

Is it fair to say your argument is basically, "if a black hole's entire existence is within an event's past light cone, then any interior events of the black hole are also within that event's past light cone"?

This is fair, we all appear to agree that finite black holes demand an "island" of spacetime which can be located in our past light cones, but whose interior contains points which are not. You both seem to feel that this is OK, and 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).

[Strange]

1 hour ago, rjbeery said:

This is fair, we all appear to agree that finite black holes demand an "island" of spacetime which can be located in our past light cones, but whose interior contains points which are not. You both seem to feel that this is OK,

I'm not sure what this "island" is. The spacetime inside the black hole is not in your past light cone. And never will be, even if the black hole evaporates. It is not points that are not in your past light cone, it is events. The difference is crucial.

It would take someone with far more knowledge than me (e.g. Markus or Mordred) to say how the spatial coordinates inside the black hole relate to those after it has evaporated. You seem to think of it like a bubble shrinking and exposing the space that was inside. But it is much more complicated than that because of the space-time curvature. For example, inside the event horizon, the radial space dimension becomes the time dimension. So it isn't clear how, or even if, you can map the spatial coordinates inside the event horizon to those where the the event horizon used to be.

For example, in Gullstrand-Painleve coordinates (which are one of the coordinate systems which are continuous over the event horizon) the spatial coordinates are effectively flowing towards the centre of the black hole. This means that as the black hole evaporates, the spatial coordinates that used to exist inside the black hole, no longer exist and have been replaced by other spatial coordinates "flowing in" from outside.

So you cannot relate a "location" inside the event horizon with one in the space after the black hole has evaporated. (Which back relates to the point about a bubble earlier: in that case you can apply the same global, cartesian coordinates to describe the situation before and afterwards. You can't do that here. When you talk about a location where the black hole used to be, that isn't the same location as when the black hole was there.)

1 hour 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).

As black holes, including the event horizon, are described by GR which requires a differentiable manifold that is obviously not the case.

The point at which the manifold is no longer differentiable is at the centre of the black hole. That is why it is called a singularity: GR no longer applies there.

[rjbeery]

3 hours ago, Strange said:

I'm not sure what this "island" is.

It's the section in the past of our spacetime diagram where a theoretical black hole temporarily existed. The original way I showed the problem was this:

The left vertical axis is the origin, r=0. This black hole is created and then eventually evaporates. Hawking wanted to represent the space r=0 after the black hole had dissipated, but you cannot normally do that with a Penrose diagram because timelike infinity is represented at the top. To see that this is a problem, consider the coordinate of the black hole completing its evaporation at t=100 in coordinate time. The point (r=0, t=100) is represented both at the event horizon formation and also after the black hole is gone.

 

 

Edited June 17, 2020 by rjbeery
wrong pic

[Mordred]

Please provide the source of the diagram above. Some of the details above need clarification.

 Another point of detail is that on causal connections one must also take care on the observer.

 To an outside observer once the EH is crossed you have reached infinite redshift. However a coordinate change can somewhat differentiate where this will occur. An EH is an apparent horizon not a true horizon. So how one defines the light one also involves the coordinate choice. Also there is a significant difference from what an observer at rest will note and an infalling observer. They will have significantly different lightcones. To make matters worse a rotating BH can have four event horizons. The Penrose diagrams also show that a rotating electrically charged BH is different from both the static and rotating BH. An infalling observer for example will see a different location of the EH as opposed to an an observer at rest.

(Black holes and causal connections are not easily described. There are non trivial factors to take into consideration)

 Hence needing further details on your diagram.

 Diagrams are no substitute for the mathematics ie the line element ds^s.

Edited June 18, 2020 by Mordred

[rjbeery]

2 hours ago, Mordred said:

(Black holes and causal connections are not easily described. There are non trivial factors to take into consideration)

 Hence needing further details on your diagram.

The diagram is from page 219 of Hawking's "Particle Creation by Black Holes" paper. The causality issue is why Penrose diagrams are useful. I'm claiming that what Hawking did with them is not mathematically valid. The vertical axis is the time parameter, and either his diagram shows a black hole forming (and evaporating) in finite coordinate time, which is not supported by any mathematics of GR, or he is showing events that occur after the infinite future (i.e. higher on the vertical axis).