Sometime ago I read an article on black holes that left me scratching my head in befuddlement. Unfortunately I didn’t save the article and therefore cannot refer to it here. In any case, as well as I can remember, it said something like the following:
It is said that two separate BHs can coalesce into a single BH, but this is not necessarily a description of what is really occurring.
The statement presupposes a specific coordinate system and foliation of spacetime that is not singular. In other words there are other equally valid foliations that say that there was only one black hole at all times. So how many BHs were there? There seems to be however many you may want. This is almost like the uncertainty in photon number and phase that exists in QM.
Many think that the black hole singularity occupies a specific point in spacetime at r = 0, but this cannot be correct, because the space and time coordinates switch at r<2M.
This means that, in the limit, the surfaces in the neighborhood of the singularity are spacelike not timelike, and therefore it is impossible for the singularity to occupy a single point in spacetime.
I have no idea if the above is total gibberish or absolute fact and would appreciate any enlightenment that anyone (Chronos?) could supply.
For 1, there’s certainly a change in the topology of the event horizon when two black holes merge. That’s good enough for me to call it separate holes at that time.
For 2, it’s flawed to say that the singularity occupies a point in spacetime, but not for that reason. Rather, one might loosely say that it occupies a point not in spacetime. 0 is simply not an allowed value for r. But you can look at r=constant spheres in the limit as r -> 0, and such spheres have surface area 4pir^2, just like you’d expect (in fact, this should be no surprise, since this is actually how r is defined in the standard black hole coordinates).
I want to preface this by saying that I don’t know much about topology in GR, so some of this may be wrong.
For #2, I think what Chronos says is mostly right, but there’s another fundamental difference here between the neighborhood of the Schwarzschild singularity and normal regions in spacetime, which is I think what the author is getting at. For a normal event Z in spacetime, like “New Year’s, Times Square”, a neighborhood of this event contains some points at timelike separations from Z, some happening before Z and some happening after Z; and some points at spacelike separations from Z. This is not the case for neighborhoods of the singularity, though. All of the points in the neighborhood of the singularity S have timelike separations from S, with S in their future.
Another way to think about this is to consider the constant-r surface which “surrounds” the singularity. In normal flat-space 3+1 spherical coordinates (t,r,theta,phi), the surface of constant r is the product of a spacelike 2-sphere (varying theta and phi) with a timelike real line (varying t); this is the infinite cylinder which surrounds the world line of the origin. But around the singularity, both the 2-sphere and the line are spacelike. So you can draw an entirely spacelike boundary separating the neighborhood of the singularity from the rest of the universe; this is not something you can ordinarily do.
For #1, I’m not so sure that the topology actually changes, though I hesitate to disagree with Chronos. The normal way to think about two colliding black holes would start with two mostly-spherical horizons, which somehow distort and merge, ending with a single mostly-spherical horizon–which certainly looks topologically different from two horizons. (No, I’m not going to mention Banach-Tarski here.:))
But the horizon of a black hole is not just any old sphere, it’s a null surface: it’s defined by the null geodesics which are unable to escape to infinity from the neighborhood of the black hole. So it seems to me that you can cover everywhere in spacetime outside of the event horizons with a family of spacelike surfaces, getting arbitrarily close to both horizons (so they are “almost” null surfaces) while staying outside them. This gives you a timelike coordinate in which there is only ever one black hole. This is kind of hard to visualize, but maybe it’s at least believable that by a small distortion of the combined horizon you can get a spacelike surface lying just outside the horizon; choosing this as a surface of constant time gives a perspective from which there is only one black hole.
i’m a new member, so please forgive me if i make some beginner’s mistakes.
i’m almost 60 now, and i’ve been obsessed with finding the right definition for the word Truth since i was about 12. another name for it is the self referred to in ‘know thyself’. about 5 years ago i had a shocking experience in which i actually ‘saw’ Truth’ itself.
to my surprise i saw that, though abstract, it’s not an idea, and also not (as the new age would have it) consciousness. it’s not some super-aware subject, but the ultimate Object.
the commodity of which it’s made is existence. its form is both massive and nonlocal. it’s the infinite mass which is the reason why no particle may be accelerated to the speed of light. other asymptotes, such as the absolute zero of temperature could also be used to describe it.
if one takes the point of view of this true mass, the implication of the asymptotes is that the created world does not touch it and does not partake of the commodity of which it is made, and does not therefore exist.
i’ve been working on a model i call mystic physics to describe what i saw. part of this model describes this ‘true mass’, and part of it describes a local version of it. the two parts of this model are similar to the two parts of Einstein’s theory of relativity. he preferred the term invariance, but relativity caught on instead, so i guess i can use that term myself.
sincerely,
baxishta
ps is there a way to attach or post a jpeg file to SDMB?
I hesitate to invoke Pauli’s Not Even Wrong criticism, and not to hijack this thread too much, but could you give some examples of real world experiments or observations that would falsify your theory?
No, this board doesn’t allow that – you have to upload the picture to a third-party site like Flickr and link to it from here.
As an aside, Ring, it’s a little unnerving when you post a question about astrophysics, since I’m more used to you providing the explanations! :eek:
thanks for asking. no, i’m afraid i can’t support my claims in any way. the closest i could come would be to reference the Indian philosophy of ajata.
the reality of the world is what is in question, so for me to find a real world example, either pro or con, would be a case of provincial logic.
as i say, i’m new here. and to be honest, my thoughts have not been well-received elsewhere. the best i can do is to be polite but unwavering in my assertions. if this approach is not encouraged here, please let me know and i’ll continue looking for the right venue.
baxishta
ps here’s a link to my facebook page, Facebook , which shows some of my work to date.
baxishta, do you understand thoroughly the discussion earlier in this thread? If not, then your contributions to theory probably are not going to be appreciated.
There’s not really a good spot on this Board for uninformed mystic pseudoscience, but you can try in IMHO. GQ is definitely out unless you want actual working physicists to tear your work apart sentence by sentence. Some won’t be polite about it.
i think i’m more a case of informed pseudoscience. i’ll bow out of SDMB gracefully unless someone is interested in hearing more, which i understand is unlikely.
for what it’s worth my experience can be duplicated, which is the purpose of mystic physics.
I know this is a zombie thread, but two black holes coalescing is some complicated-ass **** to use the vernacular.
This can only be WAG, modelling two balck holes coalescing requires supercomputers and I think that only someone who truly is an expert in GR would likely be able to give a definitive answer. But I’d say consider the infalling observer, do they hit the singualrity before or after the black holes coalesce?I think the answer is either ‘after’ or it depends on your pov.
An interesting question, but I think that the answer would depend not only on the reference frame you’re asking it in, but also on exactly how you characterize the infalling observer. An analytic answer is probably possible for a simple case like a negligible-mass observer sitting at the center of mass of two equal-mass Schwarzschild holes with no angular momentum, though. It might even be possible to draw a Penrose diagram that makes the answer immediately obvious, but I’m not awake enough right now to do that.
Omphaloskeptic, somehow or other I missed your post the first time around, but thanks for your explanation. I’m not going to say I completely understand what you’re saying, but I do sort of get it.
baxishta, don’t go away mad, but you have to keep in mind that Omphaloskeptic and Chronos are pretty much experts in GR, and your post didn’t really have anything to do with that subject.
As Exapno said, maybe another of the forums here would be more appropriate. Plus, if you have a theory that you’d like people to take seriously you’re going to have to show the math, Without the math all you’ve got is a story.
There might be an analytic solution, but not one that’s currently known.
Again thsi a bit of a WAG but it may even be simpler to consider what happens when the event horizons of a very large black hole and a very small black hole meet.
Is this equivalent to saying “everything that will ever fall into a black hole is part of the black hole’s space and time coordinates and so in a sense was ‘always’ part of the black hole”?
