How do black holes grow?

PeterDonis

This is not the standard sense of the word "simultaneous" in relativity. "Simultaneous" does not apply to things that all happen at the same point in spacetime; and all the photons you are seeing NOW are arriving at your eye at the same point in spacetime. "Simultaneous" is a term standardly used in relativity to describe events that are spatially separated, and no two events that are simultaneous in the standard sense can be causally connected; the events on your past light cone are *not* simultaneous in the standard sense.

So, for example, the event on the Sun's surface at which a photon was emitted that is just striking your eye NOW--call this event E--is *not* simultaneous with the event of your seeing it--call this event S. Event E is in the causal past of event S. But an event on the Sun's surface to the future of event E could be simultaneous with event S, depending on what simultaneity convention you adopt. By the most natural such convention for us here on Earth, the event on the Sun's surface that is simultaneous with event S would be 500 seconds to the future of event E (because 500 seconds is the light travel time, in the Earth's rest frame, from the Sun to the Earth). But other conventions are possible.

DaleSpam

Yes, you are confounding they two. You are deliberately using terminology for simultaneity, most notably the word "now", to describe causality, thereby mixing up the two separate concepts and potentially causing confusion. That is what "confounding" means.

My original objection was to your "definition of 'now'" comment, which explicitly identifies the past light cone with a simultaneity convention. You even called it a coordinate system, further emphasizing the simultaneity.

I am not distorting your statements. Nobody besides you abuses the terminology this way, as your inability to provide references shows.

Mike Holland

Yes, Peter, I understand that. But I am accused of claiming that events on my light cone are simultaneous, and I have never claimed any such silly thing.

Of course events that occur at the same time and place are simultaneous, and this is so obvious that no-one bothers to discuss it. Thats why the scientists only discuss it for spatially separated events, in which case it all depends on the reference frame.

Mike

PeterDonis

If you didn't intend to make such a claim, then DaleSpam is not the only one who finds your use of language to be, at the very least, confusing. I do as well.

It's good that you recognize that, but it wasn't obvious from your prior posts. Let me suggest a better way of wording what I think you may be trying to say:

The past light cone of the event "here and now" defines one *boundary* of our "now"; only events to the future of that boundary are candidates to be considered as part of our "now" (which specific events outside the boundary count as our "now" depends on the simultaneity convention we adopt). Similarly, the future light cone of the event "here and now" defines the other boundary of our "now"; only events to the past of that boundary are candidates to be considered as part of our "now". The standard Einstein simultaneity convention picks the set of events that are exactly "halfway between" these two boundaries as "now", but other conventions are possible, as long as they are consistent with the boundary requirements above.

harrylin

Ah, that's a little different. Some people may mean with "supernova" the phenomenon as seen on Earth, and which we ascribe to something that happened a long time ago. In scientific discussions we only say that Sirius exists because we know of no reason to assume that something happened to it during the last 10 years; we don't mean with "Sirius exists" that we observe it now.

However, the confusion between the time of observation here and the time of occurrence there is itself a recurring phenomenon in recent discussions; hopefully it will be settled in the thread on simultaneity.

Mike Holland

As a side issue, this is also why I am not happy with PeterDonis referring to the whole region between light cones as "now". All events there are certainly candidates for "now", but you need to select them by selecting a coordinate system to describe this region which you cannot view. I cannot accept the idea of causally connected events there all being referred to as "now". Not for one particular observer, anyway.

But this isn't physics. It is just the use of language.

Mike

PeterDonis

I actually did make an argument along those lines once, but it wasn't in this thread. For this discussion I agree that "now" refers to a particular surface of simultaneity, not to the entire region between the light cones.

This is a good point which I hadn't considered when I made the comments in the earlier thread I referred to above. One requirement of any reasonable concept of "now" should be that no two events in the set we label "now" can be causally connected. That makes it untenable to view the entire set of events between the light cones as "now". None of the events in that set are causally connected to the event "here and now", but there are certainly events in that set which are causally connected to each other.

arindamsinha

I have been following the discussions above, and somehow it has given rise to a new question in my mind:

• How did the concept of 'black holes' come up in the first place from GR, from a historical perspective? Was it the Schwarzschild solution/metric that gave rise to this concept? Or, was it something different?

I believe Einstein never quite accepted this particular corollary of GR, and he was not necessarily right in doing so. All the development of black hole theory seems to be post-Einstein or extra-Einstein...

Any insights on this will be very helpful, especially if there is a chronology of the development of this.

PeterDonis

A good layman's chronology, from someone in the field, is in Kip Thorne's popular book Black Holes and Time Warps. Going from memory since I don't have my copy handy, a quick chronology would, I think, look something like this (some of these items may only be mentioned very briefly, if at all, in the book, but this stuff has come up in a number of recent threads so it's fresh in my mind ):

1915: Einstein publishes his field equation.

1916: Schwarzschild discovers his solution, but he writes it in coordinates in which what we now know as the event horizon is at "r" = 0, not r = 2M. Consequently, he only discusses one region of the solution, whereas we now know (see below) that there are others as well.

1920's or early 30's: I believe Eddington, sometime during this period, came up with at least a version of what we now call Eddington-Finkelstein coordinates, but there was no follow-up for several decades. Also, sometime during this period, what we now call Painleve or Lemaitre coordinates were independently invented several times, but again there was no follow-up for several decades.

1939: Oppenheimer and Snyder publish their paper on gravitational collapse: first known model that includes collapsing matter and the vacuum region around it. However, they write their model in what we now call Schwarzschild exterior coordinates (*not* the same coordinates that Schwarzschild himself used in his 1916 paper!), and the physical nature of the coordinate singularity at the horizon (r = 2M) is not fully understood.

1939: Einstein publishes a paper showing that no stationary configuration of matter can be in a stable equilibrium unless its radius is at least 9/4 M (i.e., at least 9/8 of the Schwarzschild radius corresponding to its mass). He believes that this shows that gravitational collapse cannot occur; our modern understanding is that it only shows that a collapsing object, such as the one that appears in the Oppenheimer-Snyder paper, can't be in a stable equilibrium once its radius is less than 9/4 M.

1957: Finkelstein publishes a paper deriving what we now call Eddington-Finkelstein coordinates, and arguing that his derivation shows that the Schwarzschild solution to the Einstein Field Equation must include a region inside the event horizon, because otherwise the solution is incomplete: geodesics reach the horizon in a finite proper time, and all physical invariants are finite there, so they can't just stop without violating the EFE.

1960: Kruskal discovers that the full, maximally extended Schwarzschild solution contains even *more* regions than Finkelstein had thought: a total of four. Two of these (exterior, and black hole interior) are those covered by Eddington-Finkelstein (and Painleve) coordinates. However, Kruskal shows, by the same sorts of arguments that Finkelstein used, that in the (idealized and not physically reasonable, according to the best current understanding) case of a spherically symmetric spacetime which is vacuum everywhere, the solution is incomplete unless a "white hole" region and a *second* exterior region are also added. (These regions do *not* appear in solutions such as the Oppenheimer-Snyder model when those solutions are completed; instead, portions of regions I and II are joined to a non-vacuum region containing the collapsing matter.)

1960's: The "golden age" of black hole research: new mathematical tools are developed to study the global properties of spacetimes (i.e., solutions to the EFE), and various singularity theorems are proved which show that, if classical GR is correct, gravitational collapse starting from some reasonable initial conditions *must* form an event horizon, a black hole, and a curvature singularity at r = 0. After this point the study of black holes became "mainstream" relativity physics.

PAllen

Here is a rough chronology:

http://en.wikipedia.org/wiki/Timelin...k_hole_physics

Plenty is missing, co-discoverers, and earlier discoverers often absent, but a reasonable high level chronology.

Yes, Einstein never accepted that BH could actually form (he did not reject that they were solutions of GR). However, since all of Penrose and Hawking's work that really established they could and would form if GR is true came after his death, that isn't saying much.

arindamsinha

PeterDonis and PAllen,

This is great stuff. Thanks for the responses. This is very helpful.

One more question this raises - does this mean that the original Schwarzschild solution/metric:

1/√(1-2GM/Rc² - v²/c² - ...) or the c²dτ² = ...

is no longer considered completely adequate, and has been superceded by later work?

I believe the Schwarzschild solution is still used often, and describes some observed time dilation phenomena nicely (e.g. GPS satellites). Have there been further developments/refinements to this metric, and if so, would you be able to provide some inputs on that? Looking for something of low mathematical complexity that I can understand, not something marinated in tensors etc. hopefully )

harrylin

This is very interesting indeed. :-)

In view of the history I distinguish different "flavours" of GR:

- 1916 GR. Acceleration is truly "relative", and can be explained away by "induced gravitational fields". This was the driving force behind GR and it gave GR its name.
- Early GR, or Einstein's GR. Even Einstein seems to have abandoned 1916 GR; however he stuck to the remainder, incl. the physical reality of gravitational fields.
- Modern GR. It proposes the falling of matter inside R of black holes as well as the existence of white holes.

However, modern GR is only partially accepted: white holes are found to violate thermodynamics (says Hamilton; I never looked at that). And the falling of matter inside R violates quantum mechanics.

PS looking at the development like this from a distance, it appears that an equation has been pushed beyond its limits.

PeterDonis

Yes.

No. "Modern GR" does not consider white holes to be physically reasonable. They are valid mathematical solutions of the EFE only if the spacetime is vacuum everywhere. Nobody believes that this mathematical solution describes any actual, physical spacetime. Any actual, physical spacetime contains matter somewhere; in the case of a collapsing object that forms a black hole, the spacetime obviously contains matter.

Every equation in any physical theory has solutions that aren't physically reasonable; as PAllen and I have pointed out in the other thread that's running on this topic, and as you agreed there, you have to add additional constraints to determine which mathematical solutions are physically reasonable. If you are going to make claims about what "modern GR" says, at least make them about what the full theory, including constraints as well as mathematical solutions to equations, actually says.

Not true. Please do not make these kinds of claims when you don't fully understand what "modern GR" says.

Yes, which is one major reason why nobody thinks the mathematical solutions describing white holes are physically reasonable.

No, that part doesn't violate QM. The part that violates QM is when the quantum states reach the singularity at r = 0 and are destroyed. That violates unitarity. But just falling inside the horizon does not.

harrylin

You give a different different reason than Hamilton; I can't judge that now.
- http://casa.colorado.edu/~ajsh/schww.html
Oops indeed, thanks for the correction!

PeterDonis

Sorry, I should have clarified: I didn't mean to suggest that I thought Hamilton's reason didn't apply as well. Both what he says (white holes violate the second law of thermodynamics) and what I said (white holes are only present in the solution of the EFE if the spacetime is vacuum everywhere) are correct, and either one by itself would, IMO, be a good reason not to consider white holes physically reasonable. Both of them taken together just make the argument stronger.

harrylin

Yes; I'm just surprised that there he doesn't mention that other reason, which looks more pertinent to me.