Red dwarf systems also tend to be "Metal poor." To astronomers, "Metal" is anything heavier than helium. Not many heavy elements are typically expected in red dwarf systems, which means that large quantities of crust oxygen is not anticipated like you would expect in a more metal rich system.
That's only by the virtue of their longevity. You make it sound like it's an inherent property of being a red dwarf, whereas it's just statistics.
Regarding the source for the earlier statement, have you got something more rigorous than a one-sentence mention in a textbook? I've been hearing bits and pieces about this phase every now and then (it's called the T-Tauri event), but never could get my hands on anything more in-depth.
(The book seems nice, though. I've just bought a used copy for two bucks on Amazon.
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Sure, but you know what the fun thing is? You also cannot accelerate faster than the object before you, and you will never observe it falling into the black hole by definition, so you, by the virtue of being behind it, will also never fall into the black hole.
I'm also sure there's some problem with my argument that makes it invalid, but it's a pretty fun one.
Not feeling too comfortable in the subject, I can only tell you what I heard about it.
The problem is that you can't use the same frame of reference for the in-falling observer as you do for a stationary one. The solution where the in-falling object never crosses the horizon is only valid in the reference frame of a static observer outside the event horizon. For the in-falling observer you need to use a different set of coordinates:
http://en.wikipedia.org/wiki/Gullstrand%E2%80%93Painlev%C3%A9_coordinates@Tylui: I don't think there's anything to apologise for, but cheers.