7

Many consider naked singularities as a fundamental problem and that it should be always covered by a horizon (Cosmic censorship hypothesis). But why naked singularities are really a problem?

If we consider electrodynamics and the Coulomb potential, we have a singularity at $r=0$ but quantum electrodynamics solves the problem. General relativity being a classical theory we have also a singularity and with the hope that quantum gravity will remove it. But we don't need necessarily a horizon.

At classical level, naked singularities should not scare us. Why are they always disregarded?

Edit after the answer by John Rennie:

Thanks John Rennie for your answer. But we actually express exactly the same thing. I'm not saying that a singularity is not a problem, of course it is. But that singularity is not a problem within a classical theory because we expect or hope that the problem will be solved in the quantum regime.

Going back to my previous example, classical electrodynamics, no-one tries to hide a singularity behind a horizon but in general relativity we try to solve the singularity problem within the classical theory. The "Cosmic censorship hypothesis" tries to "solve" (most exactly hide) the problem within the classical regime.

My question then is, why not thinking that a naked singularity is a fair solution in the classical theory but the singularity would disappear in the quantum regime without necessarily imposing a horizon in the classical theory.

ziususdra
  • 71
  • 1
    "At classical level, naked singularities should not scare us." Why not? – probably_someone Dec 07 '18 at 17:22
  • Because as for the Coulomb potential, the singularity disappears once we add quantum corrections. So we know that the singularity exists only because we don't have a full description of the reality. In the same way, quantum gravity should eliminate the singularity so we should care about it at classical level. – ziususdra Dec 07 '18 at 17:40
  • "quantum gravity" - sure, but we have no consistent description of such a thing. Such a thing may not exist at all. – Maury Markowitz Dec 07 '18 at 17:54
  • @ziususdra What makes you so sure that quantum corrections will make this singularity disappear? Without the full theory it's impossible to know that. – probably_someone Dec 07 '18 at 18:05
  • Because they is already a solution in string theory, the fuzzball, which doesn't have a singularity. – ziususdra Dec 07 '18 at 19:21
  • 1
    @ziususdra Just because one possible theory doesn't have these singularities doesn't mean that the theory that actually describes reality doesn't have them. As of yet, there is no evidence that whatever flavor of string theory you're talking about makes more accurate predictions than the current Standard Model and/or GR. – probably_someone Dec 07 '18 at 20:12
  • LQG does the same, for example the papers by Carlo Rovelli which describes some Planck stars. I think this is not really the topic, people much more experts than us, all say that singularity should disappear in the quantum regime. And it is easy to get convinced. Singularity appears because during gravitational collapse, all matter goes to the same point without pressure to oppose to it but as soon as we have a quantum description, matter will not be localized at a single point so this notion of all matter at the same point looses its meaning. – ziususdra Dec 07 '18 at 20:54
  • @ziususdra A singularity is not a point. For example, a Schwarzschild singularity is an infinitely long spacelike line. Also, matter is not "localized" there, because such a singularity is not a position in space, but a moment in time. For example, is your matter "localized" at noon when time is 11am? – safesphere Dec 13 '18 at 07:04
  • @safesphere Yes, they are timelike singularities like Schwarzschild and spacelike singularities like Reissner Nordstrom. Sorry, but I don't understand the relation with the question. – ziususdra Dec 14 '18 at 19:11
  • @ziususdra The relation is that in the original version of your question before the edit you referred to the singularity as a "point" where matter "is localized". – safesphere Dec 14 '18 at 21:37
  • I just never used the word "point". I added the second part but never modified the first part ... – ziususdra Dec 15 '18 at 01:11

2 Answers2

3

Your initial assumption is wrong. Classical singularities do scare us, but we have a resolution for that problem because quantum mechanics modifies the classical behaviour at short distances. For general relativity no such safety net currently exists, though most of us believe quantum mechanics will remove the singularities in GR as well.

It is a basic requirement of a theory that if we know the state of a system then our theory can predict its future evolution. Technically this property of a theory is called global hyperbolicity. If a theory is not globally hyperbolic then causality breaks down because we cannot predict what cause will have what effect.

The problem with a singularity is that while we can calculate the trajectory of an infalling particle up to the moment it reaches the singularity we cannot predict what happens at the singularity or for any later time. This happens because the curvature tends to infinity as we approach the singularity and we can't do arithmetic with infinity.

However provided the singularity is hidden behind an event horizon the unpredictability doesn't matter because everything behind the horizon is causally disconnected from us - the unpredictability can never affect anything that we can observe. But if the singularity is not behind a horizon, i.e. it is naked, then what happens there can and will affect us. That means our theory (GR) is no longer globally hyperbolic and therefore cannot predict the future. We're in trouble!

This also happens in classical physics, and you use the example of the Coulomb potential. If we consider a positive and negative charge on a direct collision course then their equations of motion also become singular when the distance between them falls to zero, and there is no way to calculate what happens afterwards. But of course we know that we have to resort to quantum field theory at very short distances, and this removes the singularity. Panic over.

The problem is that quantum mechanics does not (currently) come to our rescue in GR because we have no theory of quantum gravity. As I mentioned at the start, I doubt you'd find a theoretical physicist who really believes singularities exist - we all think some form of quantum effect will remove them. But this is currently only wishful thinking and there is zero evidence to support it.

There is one final point to be made about causality. GR is time symmetric, and that means if we cannot predict what happens for particles hitting a singularity that also means we cannot predict what comes out of the singularity. If we observed a naked singularity we simply could not tell what it would do next.

John Rennie
  • 355,118
  • Isn't the Big Bang a naked singularity? The whole universe got out of that singularity, and of course it wasn't "predictible"! – Cham Dec 13 '18 at 12:30
  • @Cham: A spacetime is globally hyperbolic if (1) strong causality holds (essentially no CTCs), and (2) $\forall p$, $q$, the future timelike light cone of $p$ intersected with the past timelike light cone of $q$ is compact. By this definition, cosmological spacetimes are globally hyperbolic, despite the presence of the big bang singularity. That means we have predictability, in the sense of existence and uniqueness for Cauchy problems. You can define the big bang as a naked singularity if you like, but what matters is that it's not timelike. –  Dec 13 '18 at 14:45
  • Yes, I agree that the Big Bang is a spacelike singularity. But it is "removed" from the manifold (like most singularities) so of course the manifold is globally hyperbolic. But the Big Bang is still a naked singularity out of which everything came out. This is the kind of "troubles" we could get from a naked singularity, like the Reisner-Nordstrom solution with $Q > M$ for example (if I remember well, there's a gravitational repulsion, close to the naked singularity in this case). – Cham Dec 13 '18 at 15:20
  • @Cham yes, I agree, though I suspect this is going beyond what the OP was asking about. – John Rennie Dec 13 '18 at 16:18
  • 1
    @Cham : The big bang is not a naked singularity. And when you remove the singularity from the manifold (more accurately it was never a part of the manifold) you don't always get a globally hyperbolic space-time. – MBN Dec 14 '18 at 09:47
  • @MBN, could you elaborate why the Big Bang isn't a naked singularity? AFAIK, it could be "seen", theoretically. – Cham Dec 14 '18 at 13:25
  • The big bang is a naked singularity, and yes, we can't extend any predictability to the past of the big bang at all, just like you can't extend future predictibility from, say, a $a > M$ Kerr solution. – Zo the Relativist Dec 14 '18 at 18:20
  • Or, at least, it's a naked singularity in the sense that it has no horizon, and can be reached by geodesics that go to timlike infinity. – Zo the Relativist Dec 14 '18 at 20:25
  • @JerrySchirmer I think there is some confusion about precisely how to define a naked singularity, so to an extend the argument is about terminology. – John Rennie Dec 14 '18 at 20:32
  • Cham has asked a question on this topic: https://physics.stackexchange.com/questions/447308/is-the-big-bang-a-naked-spacelike-singularity –  Dec 14 '18 at 20:37
  • This answer has nothing to do with the OP. The user is correctly doing a perfect analogy. The Coulomb potential generated by an electron diverges at $r=0$, and the divergence tells us that our effective field theory breaks down. A new theory must be used at this point, indeed we have discovered Quantum Mechanics. The OP just asks why we cannot think of naked singularities in this same way as Coulomb potential singularities. – apt45 Jan 22 '21 at 04:02
0

It's also worth noting that black hole solutions with naked singularities tend to have other pathologies, like closed timelike curves, that don't directly involve the singularity, and even if you removed the singularity with a patch, these other pathologies would remain.

Zo the Relativist
  • 41,373
  • 2
  • 74
  • 143
  • That's interesting. Do you have some reference linking naked singularity and closed timelike curves. Because at least we can give some counterexamples in both sides. A solution which has CTC's and which is not a naked singularity: the Godel universe. And a solution which is a naked singularity and doesn't have CTC like Schwarzschild with M<0. – ziususdra Dec 14 '18 at 19:08
  • 1
    @ziususdra: Cosmic censorship doesn't fix the CTC problem in general (to my knowledge, there isn't a general proof that shows when CTC will show up), but it's somethign to consider in about some of these naked singularity solutions. The presence of CTC in the interior of Kerr solutions well known, but see:

    https://arxiv.org/pdf/0708.2324.pdf

     – Zo the Relativist Dec 14 '18 at 20:22
  • It's written by unknown people with only 1 citation and their conclusion is trivial and not realistic. Trivial because they consider a motion in opposite direction to BH within the ergosphere, so of course this observer would need a velocity larger than the speed of light which permits CTC. But if we assume that no-one could go faster than speed of light, this observer doesn't exist. At the same time, in realistic solution, there is a fluid collapsing, which eliminates the multiple copies of spacetime in the maximal extension and therefore I'm not sure that it would really produce such effects – ziususdra Dec 14 '18 at 21:08
  • @ziususdra I googled for the first result. It is very well known that you get closed timelike curves by traversing through the ring singularity, and therefore, in a naked singularity solution, you expose them to the general spacetime. References are readily available to any level of rigor you want. – Zo the Relativist Dec 14 '18 at 22:07
  • Yes but it is not physical, Kerr says it better than me (with my example of matter collapsing) https://www.youtube.com/watch?v=LeLkmS3PZ5g&t=26m – ziususdra Dec 15 '18 at 01:12
  • @ziususdra : of course it's not physical. It's a pathology in the spacetime which is evidence for the fact that you can't have naked singularities.Taking a pathology that is pointed out to you, and saying "but it's pathological, I don't expect that to be real!" is ridiculous. – Zo the Relativist Dec 15 '18 at 15:19
  • I fully agree but it is not the existence of a naked singularity which produces the problem but the presence of a singularity. We agree that a singularity is bad and generates problems and we hope that singularity will disappear in the quantum theory and therefore these problems too. My question is not about singularity but about naked singularity. If for a classical theory, I have a naked singularity why so much efforts to hide it behind a horizon if anyway a quantum theory will remove the singularity. – ziususdra Dec 15 '18 at 17:59
  • @ziususdra: the ctcs aren't related to the singularity. They don't intersect the singularity. They only don't affect the enveloping spacetime because they're hiddden behind the singularity. – Zo the Relativist Dec 16 '18 at 05:13
  • @JerrySchirmer This is probably a separate question that might have already been asked but why do CTCs hidden behind a horizon not scare us? They are as much a part of physics as they would be if not hidden behind a horizon, right? Thanks. –  Feb 22 '19 at 14:07
  • @DvijMankad: because no non-causility can get outside of the horizon, and so our outside world is safe from being expmosed to them. If you believe in something like the holographic principle, then you can even think of the horizons as something like an inner boundary for the universe. – Zo the Relativist Feb 22 '19 at 14:37