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So my argument goes like this:

say we have an object that is nearly at the density required for a black hole. Then we Lorentz boost into a new frame, the object is Lorentz contracted and therefore the density increases above the black hole limit.

As a mere change of frame can't have physical effects it surely can't create a black hole and therefore a moving black hole needs a larger density.

Is this correct and if it is how does this come out of General Relativity?

xray0
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Toby Peterken
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    I'm afraid your starting point is a fallacy (albeit an appealing one when using the language of relativistic mass). See https://physics.stackexchange.com/questions/3436/if-a-mass-moves-close-to-the-speed-of-light-does-it-turn-into-a-black-hole – dmckee --- ex-moderator kitten Aug 07 '19 at 21:48
  • I dimly remember reading, I think it was in Kip Thorne's "Black Holes & Time Warps", that all of the object's mass must be within the critical radius for collapse to a singularity to occur. Recall that the object is not Lorentz contracted in the directions orthogonal to the velocity vector. I'll try to look that up. – Alfred Centauri Aug 07 '19 at 22:44
  • Found it: it's the hoop conjecture. From Figure 7.2 of Thorne's book: "According to the hoop conjecture, an imploding object forms a black hole when, and only when, a hoop with the critical circumference can be placed around the object and rotated". I'll work on turning this into an answer after supper. – Alfred Centauri Aug 07 '19 at 22:54
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    Your argument shows why this cannot be correct. You cannot change the outcome by changing frames, as you correctly pointed out. – Brick Aug 08 '19 at 00:11

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