Insights Do Black Holes Really Exist? - Comments

[D2Bwrong]

Consider that a BH is not a solid object - a spiraling stream of particles collapsing to a gravitational center. In essence a vortex.

 

[Drakkith]

Consider that a BH is not a solid object - a spiraling stream of particles collapsing to a gravitational center. In essence a vortex.

Not true. A black hole exists whether there's an accretion disk of infalling material or not.

 

[Solon]

"..densely packed free neutrons"
I thought free neutrons decayed in 10.3 minutes?

 

[Drakkith]

"..densely packed free neutrons"
I thought free neutrons decayed in 10.3 minutes?

Not under the pressures encountered inside a neutron star.

 

[Nugatory]

If the black hole has used up all its matter, and it is now dying, what type of matter is squeezed into the tiny space? Are these types of matter similar to the particles that were present when the star was born? How could this matter squeezed into a tiny space create such a strong gravitational force?

At first nearly all the matter in the star is hydrogen gas, because hydrogen is by far the most common element. At the temperatures and pressures found at the center of a star, the hydrogen fuses to form helium; this reaction releases a tremendous amount of energy that resists further collapse and keeps the star burning for most of its lifetime. When the star runs out of hydrogen at the center, collapse resumes until the pressure at the center is enough to start helium fusing into yet heavier elements, releasing more energy and stopping the collapse again. However, this has to stop at some point because the heavier the element the less energy is released by fusing it; and fusing iron and anything heavier actually consumes energy instead of releasing it. Eventually the star runs out of elements whose fusion will release enough energy to resist collapse - and then the star collapses catastrophically.
Thus, at the time of collapse the star still has plenty of matter, as a mix of elements up to and including iron.

As for what happens to this matter when it collapses to down to the center of a black hole? We don't know. We have a good theory for very strong gravitational fields (general relativity) and a good theory for very small things (quantum mechanics) but no good theory for very small things in very strong gravitational fields.

 

[PeterDonis]

We pass through event horizons constantly. space-like hyper-surface is an event horizon, the future, and past light cones of any space-time event are examples of an event horizon, i.e. a boundary across which causal signals and matter can only travel one way.

None of these are "event horizons" in the sense that the event horizon of a black hole is; they are not boundaries of regions that cannot send light signals to future null infinity.

 

[jambaugh]

What the heck is "future null infinity"?
[edit] I mean by that, operationally. You must make some rather strong assumptions about cosmology to infer there is such a direction. [end edit]
Here is Ridler's original definition:

"We shall define a horizon as a frontier between things observable and things unobservable."
"An event-horizon, for a given fundamental observer A, is a (hyper-) surface in space-time which divides all events into two non-empty classes: those that have been or will be observable by A, and those that are forever outside A's possible powers of observation."
["Visual Horizons in World Models" Monthly Notices of the Royal Astr. Society. 116 (6): 662–677]

The only problem with this is that the observer must know his entire future world line to define an event horizon for him in this context. Choosing an observer at an instant (imagine the observer is very short lived as such) and you have my definition. Specifically the event horizon for a momentary observer is the past light cone of her final event-point of existence.

The point I was trying to get across is that if you were say falling into a sufficiently massive black hole crossing it's stationary event horizon, you wouldn't notice a thing. Later in your finite future you'd begin feeling the tidal effects until after a short time (circum-radius/c) your spatial universe in two directions squeezes to radius 0, you are stretched infinitely in the third and time stops at the singularity. (One may presume a theory of quantum gravity might refine that singularity in time better.)

 

[PeterDonis]

What the heck is "future null infinity"?

For the quick definition, see here:

https://en.wikipedia.org/wiki/Absolute_horizon#Definition

For the gory details, the definitive reference is Hawking & Ellis.

You must make some rather strong assumptions about cosmology to infer there is such a direction.

Yes, strictly speaking, only asymptoticallly flat spacetimes have a future null infinity, and the class of spacetimes used to describe the universe as a whole in cosmology, the FRW spacetimes, are not asymptotically flat. However, there is an analogous concept that works in Schwarzschild-de Sitter spacetime, which, since we believe our universe has a positive cosmological constant, is an appropriate model for our universe for this discussion. Roughly speaking, the black hole in Schwarzschild-de Sitter spacetime is the region of spacetime that cannot send light signals to the cosmological horizon.

Hm. I might need to add an addendum to the Insights article that mentions this.

Here is Ridler's original definition

As you will see if you consult Hawking & Ellis, or indeed any GR textbook since the early 1970s, including MTW and Wald, this definition is outdated. The term "event horizon" in the usage of any of the references I have just described is defined as I defined it in post #66.

The only problem with this is that the observer must know his entire future world line to define an event horizon for him in this context

The event horizon is not a property of an observer. It is a property of the spacetime geometry. What is true is that we must know the entire future of the spacetime geometry to know if there are any true event horizons, and if so, where they are. I make this point in the article.

The point I was trying to get across is that if you were say falling into a sufficiently massive black hole crossing it's stationary event horizon, you wouldn't notice a thing.

This is true, but it has nothing whatever to do with the definition of an event horizon.

 

[jambaugh]

The event horizon is not a property of an observer. It is a property of the spacetime geometry. What is true is that we must know the entire future of the spacetime geometry to know if there are any true event horizons, and if so, where they are. I make this point in the article.

Agreed with the first two sentences. But the last qualifier makes for a bad definition imnsho but that's a quibble about semantics and who's value system one chooses. Let me then define a causal horizon to be what I earlier defined as an event horizon rather than what your Wikipedia reference refers to as an absolute horizon.

This is true, but it has nothing whatever to do with the definition of an event horizon.

It has something to do with understanding the causal/event horizon of a black hole which was the OP issue. Consider...

A contracting spherical cloud of dust of radius just beyond its Schwarzschild radius for its mass. At its center, a strobe flashing out pulses of light which trace over the future light-cones of its pulsing events. In the space-time of this progressing collapse, these light cones are bent more and more forward (in the time direction) so that become closer and closer to a 3-cylinder (in distant time x angular x circumradial coordinates). They "flare" back out as they leave the cloud and move farther and farther away from it.

Then the future event horizon of that flash that reaches the outer surface of the cloud just as it shrinks to its Schwarzschild radius will remain forever on the resulting black hole's event horizon. This light cone has been bent into a light cylinder which is the event horizon for the history of the black hole (unless of course its mass changes.)

Any future infalling observer will see this sequence of strobe pulses including that horizon pulse as he crosses the BH's event horizon. Assuming the BH is massive enough that the tidal effects there are negligible the observer is, locally, just passing through another light cone.

So locally, as I see it, a light cone is simply an event horizon that hasn't been bent by a central mass into this cylindrical shape. I will concede the semantic debate and call it a causal horizon if you like. The event horizon of an idealized black hole is the future null 3-surface of a specific space-time event and without those asymptotic assumptions, it is qualitatively no different. Certainly not in terms of local space-time geometry.

 

[PeterDonis]

the last qualifier makes for a bad definition imnsho

Which qualifier? The one about needing to know the entire future? GR is a deterministic theory, so in any GR model you do know the entire future, so knowing where the event horizons, if any, are in the model is straightforward.

The issue, if there is one, comes when we talk about how we test whether the model matches reality. It is true that we can never know for sure that there is an event horizon in reality--we can never know for sure that the model matches reality in that respect. But we still need a term for the feature of the model in question, and "event horizon" is the term that physicists have settled on for that.

If one wants to make it absolutely clear that we are talking about the phenomenon we observe in reality, I would use the term "apparent horizon", since that basically describes what we observe in reality: a boundary around a region of spacetime into which things fall, but from which nothing is ever observed to come out. Then the issue described above can be stated as: we can never know for sure that an apparent horizon that we observe actually is an event horizon. We can construct a model in which it is, but we can never know for sure that that aspect of the model matches reality.

the future event horizon light cone of that flash that reaches the outer surface of the cloud just as it shrinks to its Schwarzschild radius will remain forever on the resulting black hole's event horizon

See my edit in the quote above. "Future light cone" is the general term for, well, the future light cone of an event: the null surface formed by the maximal future extensions of all null geodesics passing through the event. Calling it a "future event horizon" just co-opts a term which already has a different, well-defined meaning, for no good reason, since we already have the term "future light cone" for what you are talking about here.

You could say that there is a particular event at $r = 0$ in this spacetime whose future light cone is the event horizon: but that just concedes the point that not all future light cones are event horizons, only some of them.

locally, as I see it, a light cone is simply an event horizon that hasn't been bent by a central mass into this cylindrical shape. I will concede the semantic debate and call it a causal horizon if you like.

Or you could just call it a future light cone, as above. That's the standard term. I think trying to gerrymander the term "event horizon" to cover all future light cones, which is basically what you are suggesting, just obfuscates things.

As for the term "causal horizon", that is even more general, since any null surface is a causal boundary; you don't even need to consider whether that surface is part of any light cone of interest. But that also means the term is so general that it is not very useful. Usually we are not interested in all causal boundaries, but only in particular ones that have particular properties.

 

[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.)