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if singularities can be observed from the rest of space-time, causality may break down, and physics may lose its predictive power,i don't understand how it will happen?we don't have any idea what will happen at singularity.so we should not observe them.

Hare Krishna
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    Why would a singularity destroy causality? Can you elaborate what mechanism you have in mind for that? – CuriousOne May 27 '15 at 07:20
  • this is my question ? then why singularities should be cover by event horizon. – Hare Krishna May 27 '15 at 07:25
  • Because that's what GR predicts. If you can find another theory that matches all the data we have as well as GR does and that has naked singularities, that's fine, too. I am not aware that anybody has found one of those, but I might be wrong about that. – CuriousOne May 27 '15 at 07:49
  • no there are metrices that have naked singularity.http://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis – Hare Krishna May 27 '15 at 08:10
  • In that case all you have to do is to find one in nature. – CuriousOne May 27 '15 at 15:34

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Physics is based on the idea that behaviour is deterministic. That means we can take some system, write down the equations of motion that describe it, and we then know how that system is going to behave for the rest of time. Concepts like conservation of energy and momentum are deeply tied into this idea.

But if you write down the equation of motion for an object falling into a black hole, then once the object reaches the singularity the equations cannot predict what will happen next. This contradicts the basic assumptions upon which all of physics is built.

For the usual type of black holes the equations of motion actually predict that the infalling falling object takes an infinite time to reach the event horizon, and therefore never crosses it. So for us observers outside the black hole there is no problem since for us the object never reaches the singularity and our equations do work for an infinite time into the future. The problem with a naked singularity is that external observers would be able to observe the infalling object reach the singularity in a finite time. Beyond that time we would have no way to predict what happens next, which is a fundamental violation of all we hold sacred.

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John Rennie
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    Hi John Rennie. May I ask : 1)Why the fact that we cannot predict what will happen after a fall in a naked singularity permits us from acquiring that knowledge after the study of this phenomenon or 2)why our luck of prediction capability destroys causality?3) And what if we find a phenomenon where causality changes or doesn't hold-it will be a single phenomenon to be studied by us, we ave to acquire data for that single phenomenon anyway- even if we face a situation where predictability is not open. Sorry for the many words ant the 3 questions here. Thank you. – Constantine Black May 27 '15 at 08:35
  • @John will ask this as a separate question if need be, but I read (skimmed) this article which suggests that the "infinite time to fall into a black hole" is a coordinate issue and the object does fall through. (if I'm reading it right) – Xeren Narcy May 27 '15 at 23:25
  • @Constantine Black: The infinite time is a ccordinate issue, but like John Rennie already said, that problem is the problem of an external observer. The infalling observer does not have any problems after hitting the singularity after a finite time, because his whole world line ends there anyway. – Yukterez Feb 19 '16 at 16:58