How can we have a singularity, without a black hole around it? How would one form? What does it do?
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2$\begingroup$ Have you heard about the cosmic censorship hypothesis? $\endgroup$ – HDE 226868♦ Feb 3 '16 at 23:04
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$\begingroup$ By "Without a black hole around it", do you mean a naked singularity without a Kerr black hole or do you simply mean without an event horizon over the singularity? I "think" you need a kerr black hole no matter what. en.wikipedia.org/wiki/Naked_singularity $\endgroup$ – userLTK Feb 4 '16 at 2:54
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$\begingroup$ I mean, a singularity without an event horizon. $\endgroup$ – Daniel Cann Feb 4 '16 at 7:10
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$\begingroup$ Explained here: physics.stackexchange.com/questions/147034/… but the math is over my head. $\endgroup$ – userLTK Feb 5 '16 at 4:18
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Nobody likes the idea of naked singularities, as they would have a toxic effect on causality. If a singularity existed that was not separated from us by an event horizon, then not only would the future not be predictable, but the past would not be fixed. Like the grandfather paradox, it wouldn't make sense, so it cant exist. The trouble is that GR doesn't implicitly rule them out.
If a black hole is spinning fast enough, or has enough charge then it seems a naked singularity could form. Naively you may think that the centrifugal force in the first case, and the electromagnetic force in the second are sufficient to overcome gravity.
I particular if $G^2M^4/c^2 < J^2$, where J is angular momentum, M is the mass, G is the gravitation constant, and c is the speed of light. The there will be a naked singularity. For a small, stellar mass black hole would need an angular momentum of $10^{42} \mathrm{kg m^2 s^{-1}}$ to lose its event horizon
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1$\begingroup$ When you say the past would not be fixed, do you mean that all spacetimes with naked singularities contain closed timelike curves and therefore one could actually travel into one's own past light cone, or do you just mean the past state cannot be predicted (or 'retrodicted') from knowledge of the complete present state (assuming it's possible to foliate the spacetime into a series of spacelike surfaces that give the 'state' at each instant)? $\endgroup$ – Hypnosifl Apr 19 '16 at 19:14
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$\begingroup$ Since we can't actually peer into black holes yet, we try to formulate mathematical equations that explain what we have been able to observe, and infer what we haven't been able to observe. I've been wondering if maybe everything that falls into a black hole might get smashed into a 2 dimensional shell, and leave the interior empty of anything, including spacetime. Kind of like the holes in swiss cheese aren't made of cheese. $\endgroup$ – Howard Miller Apr 22 '16 at 3:46
