Do Black Holes Really Exist? - Comments

[jambaugh]

I don't disagree with anything you are saying per se. As you gather I have a different mindset about how the terms should be used. To my mind "event horizon" "causal horizon" etc should be regionally defined as that's all we can operationally test. (And "yes" thanks for the edit, I did indeed intend to say "light cone" rather than event horizon.)

I do object to your referring to my effort as "gerrymandering". I am not trying to force the definitions to fit some alternative agenda. I rather am working from a philosophical position that the relevant definitions should be "regionally" defined to be meaningful. As I pointed out, the event horizon of a black hole (idealized case) is in point of fact a "light cone" in the sense that it is the equivalent of one once the curved geometry makes "cone" meaningless.

As to the determinism of the theory, that is true excepting you include other physical forces and in particular inherent quantum nondeterminism (aside from, but all the more so if you consider actual quantum gravitation itself).

As we evolve definitions, I understand that we can't be too loose with them or we can't communicate our ideas rigorously. Yet we do evolve them so that we can communicate the corresponding evolution of ideas most efficiently. I would argue (but no longer here as we've both pretty much said our piece) that my version is of utility. I understand why you disagree but, of course, not with your reasons. The definition I used was the definition I was taught by my graduate professor so it's not my own invention.

"An 'event horizon' is a space-time boundary across which causal interaction can only occur in one direction."
(Of course, that also includes spatial 3-surfaces, not just null 3-surfaces.)

I found it clarified my understanding of the event horizon of black holes immensely in exactly the way I intended to clarify the OP's inquiry. It fits with D. Finkelstein's understanding of the gravitational field as a field of light-cones, and a black hole's event horizon as the boundary where the "futures" of all event points on its are interior to the black hole.

Yet, I am outside the research for the past two decades and thus I'm not up to speed on current conventions so I bow to your authority on current meaning within the literature.

 

[PeterDonis]

I rather am working from a philosophical position that the relevant definitions should be "regionally" defined to be meaningful.

I understand what you are saying, but I'm not convinced your preferred terminology is any real improvement over the standard terminology; and if you can't convince me, I think you've got very little chance of convincing the community of relativity physicists in general, which is what you would have to do to actually change how the term "event horizon" is used in the literature. In any case, my usage in this thread, in the Insights article, and in general in this forum is based on my understanding of the standard usage in the current literature. If the standard usage were to change, I would not object to changing my usage with it; but I think that's unlikely, at least in this case.

the event horizon of a black hole (idealized case) is in point of fact a "light cone"

Actually, this is only true for a black hole that forms from gravitational collapse, i.e., a model like the Oppenheimer-Snyder model of spherically symmetric dust collapsing. For an "eternal" black hole, i.e., maximally extended Schwarzschild spacetime, the event horizon is not the future light cone of any particular event. It's a null surface that extends indefinitely in both directions, future and past. (Actually, in this spacetime, there are two horizons; what I have just said applies to both of them.)

Also, we have so far only talked about non-rotating (Schwarzschild) holes. For a rotating (Kerr) hole, I'm not sure that the hole's horizon would be the future light cone of a single event even for a model like the Oppenheimer-Snyder model. (I actually have not seen such a model for the rotating case, so I don't know for sure about its properties, but the fact that the singularity in Kerr is a ring singularity and is timelike rather than spacelike is what leads me to state what I stated just above.)

 

[jambaugh]

[...]Actually, this is only true for a black hole that forms from gravitational collapse, i.e., [...]

In point of fact any perturbation would do. The fact of it being the future light "cone" of a singular event in my idealized example was merely a method of construction. The point I wanted to make was that in terms of local geometry it is qualitatively indistinct from a section of a future light cone of some event. I thought that point was clear given how I was ("mis")using the term in reply to the OP and I'm sorry I didn't make it more explicit.

 

[PeterDonis]

In point of fact any perturbation would do.

I'm not sure what you mean here. We have not been discussing any perturbations.

The point I wanted to make was that in terms of local geometry it is qualitatively indistinct from a section of a future light cone of some event.

Locally, it is true that there is no way of telling that a particular null surface is an event horizon.

One can, however, locally detect an apparent horizon, which is a marginally trapped surface--roughly speaking, an outgoing null surface whose expansion is zero. A generic "future light cone of some event" will not have that property.

In an idealized "eternal" black hole (one that never gains any mass and in which we ignore quantum effects so there is no Hawking radiation), the event horizon coincides with an apparent horizon. In a generic black hole solution, however, that is not the case. Again roughly speaking, when a black hole gains mass, the event horizon will be outside the apparent horizon--so by the time you locally detect that you are crossing an apparent horizon, you will already be inside the event horizon and will be trapped inside the hole. Conversely, when a black hole loses mass, as in Hawking radiation, the event horizon will be inside the apparent horizon. (In fact, there is considerable literature now exploring the possibility that Hawking radiation is actually locally generated by apparent horizons, not event horizons.)