Can Black Holes Truly Exist for Earth Observers?

[rjbeery]

1) First we shall define to exist, relative to an observer, to mean that "the object in question lies in the observer's past light cone"
2) We define a black hole to be an "area of sufficiently compressed mass such that an event horizon of non-zero radius exists"
3) Next we make the presumption that black holes exist today (for observers on Earth)
4) We recognize that all existing mass approaching this black hole currently will cross the event horizon at $$t_{crossing} = +\infty$$
5) We claim that the black hole was created at $$t_{creation}$$ where $$-\infty < t_{creation} < t_{now}$$ (i.e. some point in the finite past)
6) We recognize that an event horizon of non-zero radius requires mass to exist within it, by definition

Therefore, in order for #3 to hold, at some point in time called $$t_{dubious}$$ where $$t_{creation} <= t_{dubious} < t_{now}$$, the Earth observers must be able to claim that mass crossed the event horizon of the black hole in question (in order to satisfy #6 and #1). However, for those same observers at and prior to $$t_{creation}$$, $$t_{dubious}$$ now resides in their future light cone, and will eventually reside in their past light cone, which contradicts #4. A contradiction indicates that one of our presumptions is incorrect.

The conclusion is that either all black holes are eternal (which is the only way $$t_{creation}$$ can reside in Earth observers' past light cones), or they cannot be said to exist for Earth observers.

 

[Dale]

1) First we shall define to exist, relative to an observer, to mean that "the object in question lies in the observer's past light cone"

With this definition of exist, black holes can't exist for any exterior observer. The rest is a tautology.

Do you have a reference for that definition of "exist"?

 

[rjbeery]

With this definition of exist, black holes can't exist for any exterior observer. The rest is a tautology.

Fair enough. Is there another definition of "existence" that you would prefer, or do you subscribe to the frozen star interpretation of black holes?

 

[Dale]

Is there another definition of "existence" that you would prefer

Nope. I have never needed nor seen a scientific definition of "exist".

 

[rjbeery]

Nope. I have never needed nor seen a scientific definition of "exist".

But surely in casual conversation you and most Physicists would claim that black holes "exist", yes?

 

[Dale]

But surely in casual conversation you and most Physicists would claim that black holes "exist", yes?

Yes, but casual conversations don't have forum rules against speculation.

 

[rjbeery]

Yes, but casual conversations don't have forum rules against speculation.

So you admit that it's speculation to make a claim that black holes exist while on this forum? Noted, I'll keep an eye out.

 

[atyy]

Could #4 be wrong?

 

[PeterDonis]

1) First we shall define to exist, relative to an observer, to mean that "the object in question lies in the observer's past light cone"

Sure, pick a definition that guarantees the conclusion you like, and then claim that the conclusion you like is the only possible conclusion.

The obvious rejoinder is that a black hole "exists" if the spacetime contains an event horizon. "Event horizon" has a rigorous definition, so this is a rigorous statement.

Also, your argument makes a number of statements about the "times" that various events happen. Time is coordinate-dependent, so these statements are also coordinate-dependent; but you treat them as if they were invariant statements, which they're not.

 

[Dale]

So you admit that it's speculation to make a claim that black holes exist while on this forum? Noted, I'll keep an eye out.

Well done! But, yes, I think that existential discussions in general do not belong here, regardless of the position being taken.

It certainly isn't speculation to refer to observational evidence which is consistent with a black hole and inconsistent with anything else in known physics, and there is a lot that you can discuss without ever using the words "exist" or "real" or any other such words.

 

[PeterDonis]

Could #4 be wrong?

Actually, if I wanted to focus on a single statement as being wrong, I would pick #5. If the Schwarzschild time coordinate is being used (which it must be if #4 is correct), then the time of the black hole's creation is plus infinity, just like the time when any mass falling into the hole crosses the horizon. The Schwarzschild time coordinate maps a continuous infinity of events at the horizon to a single value, plus infinity, of the time coordinate.

OTOH, if you pick a different time coordinate, such as the Painleve time coordinate, then #5 is true but #4 is false, yes. In Painleve coordinates any mass falling into the hole crosses the horizon at a finite coordinate time, and that time will be later than the finite Painleve coordinate time at which the hole is formed.

 

[PAllen]

Fair enough. Is there another definition of "existence" that you would prefer, or do you subscribe to the frozen star interpretation of black holes?

If you had a friend visit mars, and are conversing with them with several minute signal delay, would deny the exist beyond your latest signal reception? That follows from your definition.

What if your friend is in a canyon, and you can throw message bottles to them, but they are unable to throw messages to you (they're not Randy Johnson). You saw them cross the edge of the canyon, but cannot approach it and see them inside it. Would you deny they exist and may be receiving all your messages? There is considerable correspondence between this situation and an event horizon.

 

[PAllen]

First, I reject (1) as a definition.

If you use any coordinates which (and there are an infinite number, two of which are common):

- cover both the interior and exterior of the horizon
- have a coordinate that is timelike everywhere
(SC coordinates don't cover the whole spacetime, and do not have t coordinate that is timelike everywhere - if you use SC coordinates in the interior, the t coordinate is spacelike)

then:

4 is false. t crossing is finite.

5 is true for some t now for a distant observer

6 is true for some t now for a distant observer


---

Note, the above doesn't change that nothing at or inside the horizon is in your past light cone. However, the SR definition of 'now' for inertial frames also rejects such a definition.

 

[atyy]

Actually, if I wanted to focus on a single statement as being wrong, I would pick #5. If the Schwarzschild time coordinate is being used (which it must be if #4 is correct), then the time of the black hole's creation is plus infinity, just like the time when any mass falling into the hole crosses the horizon. The Schwarzschild time coordinate maps a continuous infinity of events at the horizon to a single value, plus infinity, of the time coordinate.

OTOH, if you pick a different time coordinate, such as the Painleve time coordinate, then #5 is true but #4 is false, yes. In Painleve coordinates any mass falling into the hole crosses the horizon at a finite coordinate time, and that time will be later than the finite Painleve coordinate time at which the hole is formed.

Yes, I was thinking of something like Painleve. But since in this case he's hoping for a non-eternal black hole, I suppose we can't be talking about the Schwarzschild black hole. Are there Painleve-like coordinates for non-eternal black holes? (I'm guessing yes ...)

 

[PAllen]

Yes, I was thinking of something like Painleve. But since in this case he's hoping for a non-eternal black hole, I suppose we can't be talking about the Schwarzschild black hole. Are there Painleve-like coordinates for non-eternal black holes? (I'm guessing yes ...)

Often, I've seen BH formation discussed in ingoing Eddington-Finkelstein coordinates, or Kruskal (Kruskal can be posed as coordinate condition, allowing solution for a wide variety of initial or boundary conditions).

 

[atyy]

First, I reject (1) as a definition.

If you use any coordinates which (and there are an infinite number, two of which are common):

- cover both the interior and exterior of the horizon
- have a coordinate that is timelike everywhere
(SC coordinates don't cover the whole spacetime, and do not have t coordinate that is timelike everywhere - if you use SC coordinates in the interior, the t coordinate is spacelike)

then:

4 is false. t crossing is finite.

5 is true for some t now for a distant observer

6 is true for some t now for a distant observer


---

Note, the above doesn't change that nothing at or inside the horizon is in your past light cone. However, the SR definition of 'now' for inertial frames also rejects such a definition.

Couldn't one simply remove #4, and leave intact the OP's definition, weird as it is, since we'd no longer conclude that all black holes are eternal?

Often, I've seen BH formation discussed in ingoing Eddington-Finkelstein coordinates, or Kruskal (Kruskal can be posed as coordinate condition, allowing solution for a wide variety of initial or boundary conditions).

What's a friendly source? I've read various bits of Booth's article, but it seemed largely indigestible to me the last time I tried it.

 

[PAllen]

Couldn't one simply remove #4, and leave intact the OP's definition, weird as it is, since we'd no longer conclude that all black holes are eternal?



What's a friendly source? I've read various bits of Booth's article, but it seemed largely indigestible to me the last time I tried it.

No, OP definition 1 defines all black holes of any type or origin, to not exist. Nothing else of the argument is relevant given this definition.

Not sure what you're asking for in a reference, but I like the following collapse leading to BH:

http://www.aei.mpg.de/~rezzolla/lnotes/mondragone/collapse.pdf

 

[PeterDonis]

Are there Painleve-like coordinates for non-eternal black holes? (I'm guessing yes ...)

IIRC the coordinates used in the original Oppenheimer-Snyder paper on gravitational collapse were Painleve coordinates in the exterior vacuum region of the spacetime, matched to FRW coordinates in the interior of the collapsing object. You can do this for any spherically symmetric collapse since the exterior vacuum region in that case must be isometric to a portion of Schwarzschild spacetime by Birkhoff's Theorem.

 

[rjbeery]

First, I reject (1) as a definition.

If you use any coordinates which (and there are an infinite number, two of which are common):

- cover both the interior and exterior of the horizon
- have a coordinate that is timelike everywhere
(SC coordinates don't cover the whole spacetime, and do not have t coordinate that is timelike everywhere - if you use SC coordinates in the interior, the t coordinate is spacelike)

then:

4 is false. t crossing is finite.

5 is true for some t now for a distant observer

6 is true for some t now for a distant observer


---

Note, the above doesn't change that nothing at or inside the horizon is in your past light cone. However, the SR definition of 'now' for inertial frames also rejects such a definition.

Using other coordinate systems strikes me as a dodging of the issue because their time variables are not analogous to what we as observers consider to be 'time'. Your watch does not clock the Kruskal time coordinate, for example, there is a non-trivial conversion.
$$tanh({{t}\over{4GM}}) = V/U$$
I suppose it could, but is that much different than making a watch which simply reads $$\infty$$ and claiming that everything which will ever exist, exists currently?

 

[rjbeery]

If you had a friend visit mars, and are conversing with them with several minute signal delay, would deny the exist beyond your latest signal reception? That follows from your definition.

What if your friend is in a canyon, and you can throw message bottles to them, but they are unable to throw messages to you (they're not Randy Johnson). You saw them cross the edge of the canyon, but cannot approach it and see them inside it. Would you deny they exist and may be receiving all your messages? There is considerable correspondence between this situation and an event horizon.

In both cases, you are using your imagination to project into the future. You don't really "know" that your friend exists, and it is certainly possible that he does not (he could have been eaten by a Martian bear).

The black hole situation also differs because your friend on Mars is space-like separated, whereas the interior of a black hole lies in our infinite future for all frames external to it (in other words, there is no frame that would put it in our past).

 

[atyy]

Using other coordinate systems strikes me as a dodging of the issue because their time variables are not analogous to what we as observers consider to be 'time'. Your watch does not clock the Kruskal time coordinate, for example, there is a non-trivial conversion.
$$tanh({{t}\over{4GM}}) = V/U$$
I suppose it could, but is that much different than making a watch which simply reads $$\infty$$ and claiming that everything which will ever exist, exists currently?

It isn't dodging the issue, because you mentioned the time of widely separated events - ie. some notion of simultaneity. What a person reads on his watch is his own time, and doesn't extend to any other place without a notion of what's simultaneous.

In particular, if we go by personal watch time - since that's different for everyone - the watch time of something falling past the event horizon is finite.

 

[rjbeery]

It isn't dodging the issue, because you mentioned the time of widely separated events - ie. some notion of simultaneity. What a person reads on his watch is his own time, and doesn' extend to any other place without a notion of what's simultaneous.

No, even the concept of simultaneity does not suffice in our definition of "existence", as I mentioned in my last post; the interior of the black hole is not space-like separated from any external observer.

 

[Dale]

Using other coordinate systems strikes me as a dodging of the issue because their time variables are not analogous to what we as observers consider to be 'time'. Your watch does not clock the Kruskal time coordinate

Your watch does not clock the Schwarzschild time coordinate either. Your watch only clocks proper time.

You can take any simultaneity convention and transform the time coordinate to match the proper time of any observer covered by the chart. Your objection is invalid.

 

[PeterDonis]

Using other coordinate systems strikes me as a dodging of the issue because their time variables are not analogous to what we as observers consider to be 'time'.

Which observers? There are observers whose proper time is given directly by Kruskal coordinate time, or Painleve coordinate time, or Eddington-Finkelstein coordinate time.

 

[PAllen]

The black hole situation also differs because your friend on Mars is space-like separated, whereas the interior of a black hole lies in our infinite future for all frames external to it (in other words, there is no frame that would put it in our past).

The interior of a black hole has spacelike separation from a distant observer. This is not inconsistent with the statement that no outside observer has the EH or interior in past light cone. It does mean, for example, that if tachyons existed, the interior could send messages to the exterior.

 

[PeterDonis]

as I mentioned in my last post; the interior of the black hole is not space-like separated from any external observer.

This is not correct. For any external observer, there are events in the black hole's interior which are spacelike separated from events on that external observer's worldline.

 

[Dale]

No, even the concept of simultaneity does not suffice in our definition of "existence", as I mentioned in my last post; the interior of the black hole is not space-like separated from any external observer.

This is incorrect, it is space-like separated from external observers.

[EDIT: Wow, not even second place but third place! PAllen and PeterDonis are on top of it! ]

 

[PeterDonis]

the interior of a black hole lies in our infinite future for all frames external to it (in other words, there is no frame that would put it in our past).

This is not a correct deduction. The black hole interior is not in the past light cone of any event outside the horizon, but that's not at all the same as saying it is in the future light cone of *every* event outside the horizon, which is what the first part of the above quote asserts. The future light cone of any event outside the horizon only includes a portion of the black hole interior; it does not include the entire interior.

 

[PAllen]

No, even the concept of simultaneity does not suffice in our definition of "existence", as I mentioned in my last post; the interior of the black hole is not space-like separated from any external observer.

This is totally false. For an OS collapse, the horizon and its interior have spacelike separation from exterior observers after specific time. This follows directly from the fact the horizon and singularity are in distant observer's future light light cone (but not past light cone). Therefore, the events in the interior earlier than the ones receiving light signals from the exterior have spacelike separation.

 

[rjbeery]

Your watch does not clock the Schwarzschild time coordinate either. Your watch only clocks proper time.

You can take any simultaneity convention and transform the time coordinate to match the proper time of any observer covered by the chart. Your objection is invalid.

It isn't invalid. I'm afraid there is simply no reasonable definition of what it means "to exist" which would include black holes and exclude all of history. Do you have a semantic problem with me proclaiming that, for example, "universal heat death has occurred"?

 

[atyy]

No, even the concept of simultaneity does not suffice in our definition of "existence", as I mentioned in my last post; the interior of the black hole is not space-like separated from any external observer.

Is your question equivalent to this:

We presumably can in principle experimentally verify that the spacetime metric and matter outside an event horizon obey the Einstein equation and the equation of state for the matter. However, at least for observers outside the event horizon, the same equations suggest we cannot experimentally verify that the spacetime metric and matter inside the event horizon obey those equations?

Or, to this:

Physicists claim that observations are consistent with the existence of massive black holes in galaxy centres. What definition of exist are they using?

 

[rjbeery]

This is totally false. For an OS collapse, the horizon and its interior have spacelike separation from exterior observers after specific time. This follows directly from the fact the horizon and singularity are in distant observer's future light light cone (but not past light cone). Therefore, the events in the interior earlier than the ones receiving light signals from the exterior have spacelike separation.

I'm afraid you are mistaken. Spacelike separated events are ambiguous in their causal order, and there is no external frame in which the collapse occurred "in the past".

 

[rjbeery]

Is your question equivalent to this:

We presumably can in principle experimentally verify that the spacetime metric and matter outside an event horizon obey the Einstein equation and the equation of state for the matter. However, at least for observers outside the event horizon, the same equations suggest we cannot experimentally verify that the spacetime metric and matter inside the event horizon obey those equations?

Or, to this:

Physicists claim that observations are consistent with the existence of massive black holes in galaxy centres. What definition of exist are they using?

I like this request for clarification, thank-you. My question is more related to the latter, although I must disclose the fact that I prefer the gravastar (the original "frozen star") interpretation of what we are [not] observing in those galaxy centers.

 

[PAllen]

Using other coordinate systems strikes me as a dodging of the issue because their time variables are not analogous to what we as observers consider to be 'time'. Your watch does not clock the Kruskal time coordinate, for example, there is a non-trivial conversion.
$$tanh({{t}\over{4GM}}) = V/U$$
I suppose it could, but is that much different than making a watch which simply reads $$\infty$$ and claiming that everything which will ever exist, exists currently?

You're the one insisting on one coordinate system. The invariant facts include one that you recognize:

- the EH and interior formed from a collapse are not in the past light cone of any exterior observer, ever. (equating this to 'doesn't exist' is purely a personal philosophy; note another consequence of this is that for plausible cosmologies, you would take the view that many galaxies you infer exist from match of solution with reality, do not exist, because expansion ensures they will never be in your past light cone).

and also the following that you ignore:

- there are EH and interior events that are in your future light cone. For a given always external world line, there is a specific earliest moment from which some light signal can reach singularity.


This fact implies there are many notions of simultaneity that include the interior.

 

[PeterDonis]

I'm afraid you are mistaken. Spacelike separated events are ambiguous in their causal order, and there is no external frame in which the collapse occurred "in the past".

Yes, there is. "The past" as you are using it here is not the same as "within the past light cone". You don't appear to understand this key distinction: an event can be "in the past" of another event while still being outside the past light cone of that other event.