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Einstein-Cartan relativity

  1. Jun 28, 2010 #1
    Is this extension to GR currently considered mainstream physics? Does it offer any advantage for some specific relativity problem?
  2. jcsd
  3. Jun 28, 2010 #2
    I'm not sure what you mean by "mainstream" in this context. It is a well accepted extension. It has not been ruled out by experiment. But the vast majority of work in GR: simulations, analytic calculations, etc. don't use this extension.

    This is also sometimes called the "torsion" extension of GR. In my experience, when Einstein-Cartan comes up in conversation it usually is just implied by people mentioning non-zero torsion is allowed. In fact, loop quantum gravity is actually a quantum gravity for Einstein-Cartan, and not vanilla GR. So in some sense, this extension to GR is "trivial" enough that people seem to just refer to it as GR at times.

    To explain why a bit more, if you look at the equations you will see torsion cannot "propogate" or exist where there isn't matter. It is a local property. To say this even more strongly, the vacuum equation from Einstein-Cartan is the same as that of GR.

    And now, some comments beyond what I can understand in the math myself:
    Some advantages is that without torsion it can be difficult to allows spinor matter to be included in GR. Depending on who I read or talk to, the statement of this changes, so I am not sure how much fermions necessitate the Einstein-Cartan extension. Actually, I'd love it if someone who understands QFT and GR well enough to comment directly could clear this issue up for me.

    Anyway, I hoped that answered at least some of your question TrickyDicky.
  4. Jun 28, 2010 #3
    Thanks JL. I read somewhere that the Cartan extension did not allow singularities nor propagation of gravitational waves (but I don't know for sure if this is the case.maybe someone can clarify this) and since these are probably the most active research fields in GR, I figured it might not be "mainstream" in this context.
  5. Jun 28, 2010 #4
    Here's a handy guide to evaluate such claims: without torsion, Einstein-Cartan reduces to GR. So any solution to GR is also a solution to Einstein-Cartan (but obviously, this is not necessarily true the other way around).

    This means Einstein-Cartan can't avoid features of solutions in GR. And therefore the comments you read must be wrong.

    The propagation comment may have been taken out of context though. What you may have read was something along the lines that torsion can't propagate in Cartan-GR, which is true in vacuum since torsion must be zero in vacuum.
  6. Jun 29, 2010 #5
    I found an interesting outline of the EC theory with some allusion to what I read about singularities in GR with torsion.

    From: http://www.fuw.edu.pl/~amt/ect.pdf page 11

    "In the presence of spinning matter, Teff need not satisfy the positive energy conditions,
    even if T does. Therefore, the classical singularity theorems of Penrose and Hawking can
    here be overcome. In ECT, there are simple cosmological solutions without singularities."
  7. Jun 29, 2010 #6


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    I have a slight familiarity with this subject and read these posts with interest. Thanks for the ref. TrickyDicky, it looks solid. On the question of gravitational waves, can one get radiation in the EC vacuum ? Since it's possible to have a non-symmetric energy-momentum tensor in ECT solutions, and it seems some kind of asymmetry is required, wouldn't make sense to look for a radiating solution with a source in EC gravity ?

    In one of my many speculative calculations I got the EMT of a symmetrically rotating matter field and added a tiny 'wobble'. The EMT became un-symmetric which was something of a shock, since I was trying to work in the GR context and the EMT was immediately ruled out.
  8. Jun 29, 2010 #7
    It is interesting to see that EC provides enough freedom to avoid some general proofs that apply in GR of the inevitability of singularity formation behind some event horizons. Thanks for sharing TrickyDicky.

    I misunderstood what you were saying before. When you said "Cartan extension did not allow singularities" I thought you meant you found a source claiming singularities cannot form in EC. Since all GR solutions are solutions in EC, that of course is incorrect. But I see now that you just meant that while there are blackholes with singularities in EC like in GR, it is also possible to have blackholes without singularities in EC unlike in GR.

    Maybe I'm misunderstanding the thrust of your questions here, but I think this was already answered.

    EC vacuum = GR vacuum.
    The EC vacuum is torsionless, and therefore reduces exactly to GR. So torsion cannot propagate through vacuum, and the gravitational wave solutions in EC vacuum are restricted to those of the GR vacuum.
  9. Jun 30, 2010 #8
    Well, is a blackhole without singularity still a black hole? Don't think so.
  10. Jun 30, 2010 #9
    Off course we are arguing definitions but the core idea about a black hole is the existence of an event horizon, a one way membrane. That is why it is called black because no light can escape from it. So from that perspective I see no reason why a singularity free area shielded by an event horizon cannot be called a black hole.
  11. Jun 30, 2010 #10
    I thought the event horizon was linked to the singularity,you can't have one without the other, coming both from the Schwarzschild interior solution. But maybe I misunderstood something.

  12. Jun 30, 2010 #11
    The event horizon for a blackhole forms before the singularity forms. So they aren't strictly linked even in GR like you seem to be imagining.

    The "link" between the event horizon and singularity is from the classical singularity theorems of Penrose and Hawking which you mentioned before, which makes it possible in GR to show once an event horizon forms it is inevitable a singularity forms. What is great about their theorems is the generality of them. Instead of solving for detailed situations, they used topological arguments and therefore didn't need to assume any particular distribution of matter. They only needed to make some reasonable assumptions about the form of the stress energy tensor (usually called energy conditions).

    The paper you cited says that EC gravity can violate these energy conditions in certain circumstances, and thus it is possible to bypass Penrose's singularity theorem. This means if an event horizon forms in EC, it does not necessarily mean a singularity forms. Of course singularities still can form, it just means the generality of the singularity formation inevitability is no longer guaranteed.
  13. Jul 1, 2010 #12
    Theoretically, is there such a thing as a black hole without central singularity and with an event horizon? (That is what I was refering to in my last post) That is intriguing. Would that be a "grey hole?
  14. Jul 1, 2010 #13
    Imagine that for some reason in EC the ring singularity in the rotating BH in not a singularity at all, but just is very dense. From the outside, it would be a normal Kerr black hole with a horizon.

    I dont see how horizons are linked to the singularities. Another good example - cosmological horizons. They exist without any singularities.
  15. Jul 1, 2010 #14
    Aha. One thing though, a Kerr black hole does have a ring singularity. I can imagine what you say from the outside, but if it indeed didn't have a singularity it wouldn't be a black hole, would it?

    Good point, and yet I don't know if a cosmological observable horizon can be exactly equated to a black hole event horizon. I guess the BB singularity won't count in this case.
  16. Jul 1, 2010 #15
    Cosmological horizon is not related to the Big Bang at all. It is a result of accelerated expansion.

    Could you explain why? The very notion of event horizon is that it is absolutely irrelevant what is inside, because it does not affect the outside. Also, as other posters have mentioned, EH forms before the singularity forms. SO fo some time blahck hole does not have singularity inside.
  17. Jul 1, 2010 #16
    Well, I wouldn't be so extreme, if it is absolutely irrelevant what is inside why describe the interior of a black hole at all.
    Here is the description of BH singularity from wikipedia:
    "At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite.The singular region can thus be thought of as having infinite density.
    ...any star collapsing beyond a certain point would form a black hole, inside which a singularity (covered by an event horizon) would be formed"
    Still if you have an example of a black hole (stabilized , not in the process of being formed) without singularity, please point me to it.

    This is interesting, could you please back it with some citation or specific reference?
    In that case it would be interesting to know from wich exact moment is the object properly considered a black hole.
  18. Jul 1, 2010 #17
    1 BH has EH and Singularity. Hence Singularity is needed for EH to form.
    Car has wheels and engine. Hence Engine is required to have wheels :)
    Here is your logic.

    2 Here is my favourite pic.
    [PLAIN]http://www.valdostamuseum.org/hamsmith/DFblackIn.gif [Broken]

    Even more obvious in Kruskal coordinates:

    Note that however the very notion of 'exact moment when' is not well-defined in curved spacetimes.
    Last edited by a moderator: May 4, 2017
  19. Jul 1, 2010 #18
    To back up Dmitry's comments here. Just because in GR, a blackhole will eventually have a singularity inside, doesn't mean the EH can't form before the singularity exists. Consider a collapsing non-interacting dust cloud. The EH will form before the singularity forms. While there are issues of declaring simultaneity, there are not issues in declaring time ordering for time-like separated points.

    Also, please note that part of this thread is about Einstein-Cartan gravity's ability to sidestep some of the Penrose and Hawking singularity theorems. (Which are what allow us to declare the inevitability of singularities in blackholes.)


    This thread is getting really strange. Several people have answered questions, but you move on to other questions without resolving or accepting answers from previous questions.

    Because terminology issues were identified early, one poster even stated what we meant by blackhole in an attempt to clarify. You seem to have rejected this. So please help us out here. If a dust cloud collapses and a closed event horizon forms, do you not consider this a blackhole? What definition are you using for a blackhole?

    Secondly, you seem to want to discuss EC gravity, but then counter our answers with comments solely applicable in GR. Much of this confusion seems to stem from misunderstanding of the Penrose and Hawking singularity theorems.

    Can you please state for us, in your own words, what the Penrose and Hawking singularity theorems tell us?

    These are interesting topics, and there are obviously people willing to discuss with you. But we need to correct some terminology and GR understanding issues before moving on to EC. People are asking you questions because you seem to be looping around to questions already asked and answered. We can't help if we don't understand where the disconnect in communication is. We aren't asking questions to challenge you in an argument; we are asking questions so we can hopefully understand you better.

    The whole point of Hawking's singularity theorem was showing the causal topology in our universe demanded a singularity. This is what makes the big-bang hypothesis so robust in GR. We don't need to make assumptions about matter distributions back then.

    Hawking basically used Penrose's theorem and was able to "apply it in reverse" to show that there is a past singularity for all worldlines in the observable universe according to GR.

    Your main point is correct though. Not all causal horizons are linked to singularities though. A more appropriate example would be Rindler horizons.
    Last edited: Jul 1, 2010
  20. Jul 1, 2010 #19
    Your post is really weird. What questions have I not been answering? . Not a single one, I just reread the posts, the only one asking questions was myself until your last post.
    I just posted a very simple reference about black holes from the wikipedia to avoid any confusion. My questions are simple ones though you keep making strange claims, I just showed a source that seems to say there are no blackholes in EC relativity, but you wanna turn it around to make it mean a different thing. Well, that is your legitimate opinion, the logical next step for me is to ask if a blackhole without singularity makes sense. And that is what I have asked and have been properly answered.

  21. Jul 1, 2010 #20
    If they sound strange, then there are communication issues. The most basic of which is, we seem to have different understandings of singularities and blackholes even in GR. This also seems to be causing you to misunderstand that paper you found on EC gravity.

    It does not say that. You are deeply misunderstanding. I and others are trying to help, but we can't seem to figure out what it is you are misunderstanding.

    Let me make this more explicit:
    1] Any solution in GR is automatically a solution in EC gravity. This means anything you call a blackhole in GR, must also be possible in EC gravity. Do you understand and agree with this?

    2] The Penrose singularity theorem shows that in GR once the event horizon of a black hole forms, the formation of a singularity is inevitable in the future. This theorem doesn't assume any particular matter distribution, but does make some reasonable assumptions about the form of the stress-energy tensor. Do you understand and agree with this?

    3] The paper you gave does not show "there are no blackholes in EC relativity" (as should be obvious from #1 alone). It shows instead that there is a loophole in the Penrose singularity theorem, which means we can't use this to prove a singularity must form if a closed event horizon of a black hole forms in EC gravity. This does NOT mean singularities cannot form, nor does it mean event horizons cannot form. Do you understand and agree with this?

    4] EC vacuum equations = GR vacuum equations. This means outside of an event horizon in vacuum, even if EC allows some non-singularity static solution of matter to form inside the event horizon, the solution outside must still be a solution of GR vacuum equations. This is why Dmitry67 says "Imagine that for some reason in EC the ring singularity in the rotating BH in not a singularity at all, but just is very dense. From the outside, it would be a normal Kerr black hole with a horizon." Do you understand and agree with this?

    All I did was basically collect and restate things that have already been discussed that you seem to not have understood. So let's take a step back and try to figure out where the misunderstanding is stemming from. If after thinking about it awhile, you still disagree with any of those 4 paragraphs, please say so and explain why.
    Last edited: Jul 1, 2010
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