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This question has been bothering me a bit. I know that neutrinos have super small mass and they interact via the weak force. Since they have a non-zero mass, they should be affected by black holes and their paths should be affected by them.

Suppose we have a neutrino of any flavor traveling directly to the coordinates of the singularity of a black hole... or its cross sectional impact includes the black hole coordinate. Basically, its going straight towards a black hole...

Given that a black hole has so much mass and is so dense, it surely must be able to interact with a neutrino, right?

What are the conditions for neutrinos to get trapped in a black hole, or not?

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If they go in the horizon they don't come out. Just the same as anything else. – Michael Brown Mar 22 '13 at 7:53
Yep, even if they were fully massless, they'd be screwed – twistor59 Mar 22 '13 at 8:01

Yes. Not even the light, which has no mass, can escape when it goes too near to a black hole, let alone the (tinily) massive neutrinos. Also neutrinos interact via the weak force, as you correctly state, but they also interact via gravitational interaction (even if they were massless they would, obviously when speaking about black holes one has to use General Relativity as opposed to Newtonian Mechanics).

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Like zakk says, the key here is to not just think the black hole's gravity as a force that affects objects based on their mass, rather as a curvature of space-time. In this sense, everything, regardless of mass, is trapped in a black hole because it warps space-time in such a way that the area inside the horizon is essentially cut off from the universe. Light doesn't even escape--not due to the gravitational force, rather because of the way that space and time don't allow it a way out.

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