# Are ALL black holes eternal?

1. Mar 10, 2013

### 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.

2. Mar 10, 2013

### Staff: Mentor

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"?

3. Mar 10, 2013

### rjbeery

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

4. Mar 10, 2013

### Staff: Mentor

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

5. Mar 10, 2013

### rjbeery

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

6. Mar 10, 2013

### Staff: Mentor

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

7. Mar 10, 2013

### rjbeery

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.

8. Mar 10, 2013

### atyy

Could #4 be wrong?

9. Mar 10, 2013

### Staff: Mentor

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.

10. Mar 10, 2013

### Staff: Mentor

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.

11. Mar 10, 2013

### Staff: Mentor

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.

12. Mar 10, 2013

### PAllen

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.

13. Mar 10, 2013

### 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.

14. Mar 10, 2013

### atyy

Yes, I was thinking of something like Painleve. But since in this case he's hoping for a non-eternal blackhole, 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 ...)

15. Mar 11, 2013

### PAllen

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).

16. Mar 11, 2013

### atyy

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.

17. Mar 11, 2013

### PAllen

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

18. Mar 11, 2013

### Staff: Mentor

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.

19. Mar 11, 2013

### rjbeery

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?

20. Mar 11, 2013

### rjbeery

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).