Can Black Holes Truly Exist for Earth Observers?

[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.

 

[PeterDonis]

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

They're using the one I gave in post #9: a black hole "exists" if the spacetime contains an event horizon.

 

[Dale]

It isn't invalid.

It is invalid. PAllen is correct to point out that there exist a class of coordinate systems where your coordinate-dependent statements are not true.

You are asserting a physical preference for a specific set of coordinates that simply is not valid in GR. The Schwarzschild coordinates are no better nor worse than any other valid coordinate chart covering the same section of the manifold, which is essentially one of the basic principles of GR. Hence, your objection to PAllen's criticism is invalid.

Do you have a semantic problem with me proclaiming that, for example, "universal heat death has occurred"?

Can you produce a valid coordinate system where the universal heat death is simultaneous with yesterday?

 

[rjbeery]

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.

It is in the future light cone of every event outside of the horizon TODAY. I'm talking about existence and what we mean by that word today. It is nonsensical to claim that something exists today only because it will in the future.

 

[PAllen]

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.

Note, I think many physicists think the GR description of BH interior is incorrect; some that the horizon description is wrong (though this is getting less tenable as observations are closing in on the horizon). Is the discussion here quantum modifications to GR (gravastar is a variant of these), or what classical GR predicts. I (and I think others) have been answering in the context of classical GR. You need to clarify the basis for your discussion.

 

[PeterDonis]

Do you have a semantic problem with me proclaiming that, for example, "universal heat death has occurred"?

Yes. This is the flip side of the error you're making about "past" vs. "past light cone". An event can be "in the future" of another event without being in the future light cone of that event; but if it is, the events must be spacelike separated. The universal heat death is in our future light cone, so it's not spacelike separated from us "now".

 

[rjbeery]

They're using the one I gave in post #9: a black hole "exists" if the spacetime contains an event horizon.

Contains "when"?

 

[PeterDonis]

It is in the future light cone of every event outside of the horizon TODAY.

No, it isn't. Assuming that the classical GR picture is correct as regards there being a black hole at the center of the Milky Way galaxy, there are events in the interior of that black hole which are *not* in the future light cone of the event of you sitting at your computer right now, or of any other event outside the horizon that is simultaneous with that event. This is actually true for *any* simultaneity convention you choose, not just the Schwarzschild coordinate simultaneity convention, which is the one you appear to prefer.

 

[PeterDonis]

Contains "when"?

There is no "when". The spacetime is a 4-dimensional geometric object; the event horizon is an invariant geometric feature of that geometric object. The statement "the spacetime contains an event horizon" is therefore an invariant geometric statement; it's not associated with any "time". It's just a geometric fact, like the fact that the Earth's equator is a great circle.

 

[rjbeery]

Note, I think many physicists think the GR description of BH interior is incorrect; some that the horizon description is wrong (though this is getting less tenable as observations are closing in on the horizon). Is the discussion here quantum modifications to GR (gravastar is a variant of these), or what classical GR predicts. I (and I think others) have been answering in the context of classical GR. You need to clarify the basis for your discussion.

Completely fair. I focus on philosophical questions about the nature of reality irrespective of which mathematical model we use, and that can cause miscommunication.

 

[Dale]

Personally, I have no problem with rjbeery's definition of "exist". As far as I know, it is not an important concept scientifically and there isn't a standard scientific definition, so IMO you should be free to define it how you like.

The way you have chosen to define it means that black holes tautologically do not exist for exterior observers. That poses no problems whatsoever for the theory since the theory does not predict that they should exist according to that definition.

 

[Dale]

I focus on philosophical questions about

This forum is for science, not philosophy. Please restrict your questions to scientific ones.

 

[PAllen]

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".

You are mistaken. You are now arguing against mathematical fact. Spacelike separation means: neither in your future light cone, nor in your past light cone. There are many interior events in this category (as well as interior events that are in your future light light cone). In general, there exist timelike interior world lines that go from outside your future light cone right now, to inside it.That is, there would exist an interior free faller who would get a signal you send now at a specific time on their watch after crossing the EH and before reaching the singularity. Events on this world line earlier than this signal receipt have spacelike separation to you now.

 

[PAllen]

It is in the future light cone of every event outside of the horizon TODAY. I'm talking about existence and what we mean by that word today. It is nonsensical to claim that something exists today only because it will in the future.

Actually, I find it perfectly sensible to claim that if a theory predicts that something will exist in the future, there is some (possibly future) time I would declare it to exist in the present (per that theory). However, this debate is not constructive because it is Ontology not physics.

 

[rjbeery]

You are mistaken. You are now arguing against mathematical fact. Spacelike separation means: neither in your future light cone, nor in your past light cone.

This is interesting because you are all saying the same thing; I do not question your mathematical abilities, so I think there is a miscommunication here. I'm wondering if there is a semantic issue, or I'm using terminology incorrectly, but the interior of the event horizon in the future surely cannot be considered to be the same spacetime location as that of today when we are postulating its existence? A portion of the event horizon interior can be light-like separated from us, I will obviously admit, but are you claiming that the remaining portion of its interior is space-like separated from us "now"?

 

[rjbeery]

Actually, I find it perfectly sensible to claim that if a theory predicts that something will exist in the future, there is some (possibly future) time I would declare it to exist in the present (per that theory). However, this debate is not constructive because it is Ontology not physics.

Yes, I've already gotten what I intended to from the OP. Thanks for your input

 

[PAllen]

This is interesting because you are all saying the same thing; I do not question your mathematical abilities, so I think there is a miscommunication here. I'm wondering if there is a semantic issue, or I'm using terminology incorrectly, but the interior of the event horizon in the future surely cannot be considered to be the same spacetime location as that of today when we are postulating its existence? A portion of the event horizon interior can be light-like separated from us, I will obviously admit, but are you claiming that the remaining portion of its interior is space-like separated from us "now"?

There is one definition of spacelike separation carried over from SR to GR: events between my past light cone and by future light cone of this moment, have spacelike separation from me now. For the BH interior, there are events in my future light cone and events not in my future light cone, such that a timelike patch connects these spacelike separated events to the ones in my future light cone. The only peculiar thing is that no interior event will ever be in the past light cone of an exterior event (it will always be a mix of events with spacelike separation from you, and events in your causal future; the former come before the latter on interior timelike curves that connect them). To me, the 'never in your past light cone' peculiarity is nothing but a consequence of gravity being so strong that light cannot escape.

 

[rjbeery]

There is one definition of spacelike separation carried over from SR to GR: events between my past light cone and by future light cone of this moment, have spacelike separation from me now. For the BH interior, there are events in my future light cone and events not in my future light cone, such that a timelike patch connects these spacelike separated events to the ones in my future light cone. The only peculiar thing is that no interior event will ever be in the past light cone of an exterior event (it will always be a mix of events with spacelike separation from you, and events in your causal future; the former come before the latter on interior timelike curves that connect them). To me, that is nothing but a consequence of gravity being so strong that light cannot escape.

We've basically hammered the same point from many different angles, but just because something is in my future light cone does not mean it exists today when we discuss it over coffee. Additionally, the interior of the event horizon is not spacelike separated from us now if we use the wikipedia definition:

Generally, the events are considered not to occur in each other's future or past. There exists a reference frame such that the two events are observed to occur at the same time, but there is no reference frame in which the two events can occur in the same spatial location[...]Like the proper time of time-like intervals, the proper distance of space-like spacetime intervals is a real number value.

You and DaleSpam seem to apply the first sentence but not the remaining. The proper distance between any external observer and the portion of the interior of the event horizon which is not like-like separated is infinite, which is not a real number value. Additionally, the causal order is not ambiguous. In a strange way it appears that a some of the internal portion of the event horizon is neither time-like, space-like, nor light-like separated from us. All the more reason to question its existence, IMO, but this is boiling down to a semantic/philosophical issue which has been clearly pointed out to me as being outside the scope of this forum category.

 

[PeterDonis]

A portion of the event horizon interior can be light-like separated from us, I will obviously admit, but are you claiming that the remaining portion of its interior is space-like separated from us "now"?

*A* portion of the interior is, yes. More precisely: take any event outside the hole's horizon in the vacuum region (i.e., after the object that originally collapsed to form the hole has collapsed--to be more precise here as well, this is an event in the exterior vacuum region that has at least some portion of the collapsing matter, *before* it reached the horizon, in its past light cone). Call that event E. Then the interior of the black hole can be divided into three portions: a portion that is in the future light cone of event E, a portion that is lightlike separated from event E (on the boundary of E's future light cone), and a portion that is spacelike separated from event E.

[Edit: In view of your comment in the last part of post #52, I should clarify that these are the *only* three portions: together they comprise the entire black hole interior.]

I don't think PAllen or DaleSpam have said anything different from the above; but perhaps putting it in these more direct terms will help.

 

[PAllen]

We've basically hammered the same point from many different angles, but just because something is in my future light cone does not mean it exists today when we discuss it over coffee.

Exists is Ontology not physics. I thought we were going to try to stick to physics and math. Spacelike has a precise mathematical definition.

Additionally, the interior of the event horizon is not spacelike separated from us now if we use the wikipedia definition:

wikipedia is not a reliable reference.

You and DaleSpam seem to apply the first sentence but not the remaining.

What you are misunderstanding is that this wording must be modified in going from SR to GR, because there are no global frames in GR (frames are strictly local in GR). There are only global coordinates in GR. Thus, this statement becomes, there is a coordinate system such that two spacelike separated events are simultaneous. And also, the last part about no frame where they are in the same location translates, in GR, to there does not exist a timelike (or lightlike) path connecting them. Thus the concept of spacelike everyone here has been using is precisely conformant to the GR expression of this SR wording you've grabbed.

The proper distance between any external observer and the portion of the interior of the event horizon which is not like-like separated is infinite, which is not a real number value.

Again, simply false. The proper distance along any spacelike path connecting exterior and interior is finite.

Additionally, the causal order is not ambiguous.

False yet again. If an interior event receives a light signal from you, the event of your sending it is clearly in its past, and it is in your future. So, for an event earlier on a timelike world line through this event, the situation is that either of you may consider any time ordering you want. All you know is that it is before an event known to be in your future (before, because it occurs earlier on a timelike world line than an event you do know is in your future).

In a strange way it appears that a some of the internal portion of the event horizon is neither time-like, space-like, nor light-like separated from us.

Utter nonsense. You really need to actually read at least a first course in GR before making such statements.

All the more reason to question its existence, IMO, but this is boiling down to a semantic/philosophical issue which has been clearly pointed out to me as being outside the scope of this forum category.

Besides the philosophy, you continue to make mathematically false statements about what classical GR says. If, instead, you want to raise a discussion about where you think GR breaks down, that is a whole different discussion, that can occur scientifically if you are careful. The literature on gravastars (which require quantum corrections to classical GR) is a perfectly acceptable topic for these forums - it has been published in peer reviewed journals, and is not considered crank science.

 

[Dale]

A portion of the event horizon interior can be light-like separated from us, I will obviously admit, but are you claiming that the remaining portion of its interior is space-like separated from us "now"?

Yes. Take the standard static black hole spacetime and any event, A, outside the EH. There are events on the inside of the EH which are timelike separated, lightlike separated, and spacelike separated from A. The lightlike separated events are the ones which can receive a flash of light emitted at A. The timelike ones are those after the lightlike ones and the spacelike ones are those before.

 

[Dale]

The proper distance between any external observer and the portion of the interior of the event horizon which is not like-like separated is infinite, which is not a real number value.

False.

it appears that a some of the internal portion of the event horizon is neither time-like, space-like, nor light-like separated from us.

False, although I wonder if in some more complicated manifolds it could be true.

 

[PeterDonis]

False, although I wonder if in some more complicated manifolds it could be true.

It's hard to see how it could be true unless the manifold were really pathological, with multiple singularities or discontinuities that prevented lightlike geodesics from being extended indefinitely. If you can extend lightlike geodesics indefinitely from a given event, you can use them to partition the spacetime so the causal separation of every event from the given event is well-defined and has a single definite value (timelike, lightlike, or spacelike).

OTOH, there is at least one obvious example of a class of spacetimes where a pair of events can have *multiple* causal separations: any spacetime with closed timelike curves, such as the Godel universe.

 

[rjbeery]

Yes. Take the standard static black hole spacetime and any event, A, outside the EH. There are events on the inside of the EH which are timelike separated, lightlike separated, and spacelike separated from A. The lightlike separated events are the ones which can receive a flash of light emitted at A. The timelike ones are those after the lightlike ones and the spacelike ones are those before.

Question: if we exclude black holes, does the GR definition of "space-like separated" coincide with the definition I gave?

 

[PAllen]

False.

False, although I wonder if in some more complicated manifolds it could be true.

Certainly, in a traversible wormhole spacetime, you have events with both spacelike and timelike geodesics connecting them. Allowing for light going through the wormhole, it seems you might not have light cones with reasonable properties - e.g. interior, exterior. [Of course, exotic matter is required, but that's not a limiting factor for mathematical GR].

However, as we know, collapsing matter (at least in scenarios similar to OS collapse) produces no wormholes. Further, the wormhole in the eternal Kruskal geometry connect events on different sheets that have no other connection; thus it does not create causal ambiguity (events that can be both spacelike and timelike in their relationship).

 

[PeterDonis]

Question: if we exclude black holes, does the GR definition of "space-like separated" coincide with the definition I gave?

If you mean the Wikipedia definition, I would say no. The GR definition is just the generalization of the SR definition to curved spacetimes where there are no global inertial frames. But the correct invariant way to do the generalization is to use light cones, not reference frames. Given any event, the past and future light cones at that event are defined by taking all future and past directed null geodesics from the event and extending them indefinitely. Events are then spacelike separated from the given event if they are outside both the future and the past light cones of that event.

Note that this definition applies in any spacetime, whether a black hole is present or not, and it doesn't require defining any reference frames. The light cones are invariant features of the geometry of spacetime, so they can be defined independently of reference frames.