Recently, I read a quora post in which the OP asked the following question: Can a black hole be formed from accelerating a body and increasing its relativistic mass to the level of a Schwarzschild black hole? This question had me confused because of an apparent conflict of principles:

  1. On the one hand, a well received answer to the quora post suggests that formation of black holes are only dependent upon the invariant rest mass, instead of the relativistic mass. Therefore, acceleration of any body to arbitrary speed would not cause a black hole to form. (See: https://www.quora.com/Is-it-possible-to-accelerate-matter-so-much-that-it-becomes-a-black-hole-in-one-frame-of-reference-and-not-in-another)

  2. On the other hand, a quick search on wikipedia indicates that kugelblitz (black hole formed from concentration of energy, possibly with zero rest mass) is theoretically possible.

So my questions are:

  1. Are there theoretical models for how a kugelblitz could possibly form? (The wikipedia page mentioned Wheeler's geons. But I do not have access to his paper and cannot tell if geon solutions are actually black hole solutions in any sense)

  2. If the answer to question 1 is yes, energy can indeed create black holes. So, from some reference frame A moving rapidly away from the earth (or really anything for that matter), will the earth have enough energy density to become a black hole in A?

Personally I believe that both answers should be no. But I'd love to hear from experts who know a lot more to judge.

  • $\begingroup$ Ball lightning has nothing to do with black holes. Did you look at the multiple questions about this topic on our site? $\endgroup$ – CuriousOne Jul 13 '16 at 10:22
  • $\begingroup$ Can you give a link please? $\endgroup$ – Zhengyan Shi Jul 13 '16 at 10:32
  • $\begingroup$ @CuriousOne I guess this is the kugelblitz the OP refers to: en.wikipedia.org/wiki/Kugelblitz_%28astrophysics%29 $\endgroup$ – Michał Politowski Jul 13 '16 at 10:35
  • $\begingroup$ The questions of whether light can form a black hole and whether fast-moving masses can appear as black holes are disjoint, and the latter is a duplicate of this question. Please ask only one question per post. $\endgroup$ – ACuriousMind Jul 13 '16 at 14:42
  • $\begingroup$ @MichałPolitowski: That is total nonsense put on wikipedia by someone who is into pseudo-science. $\endgroup$ – CuriousOne Jul 13 '16 at 15:33

A fast moving mass will not become a black hole. See the existing question If a 1kg mass was accelerated close to the speed of light would it turn into a black hole? for a discussion of this.

However suppose you take two fast moving 1kg masses moving in opposite directions and collide them. In the centre of mass frame you have the original rest masses, i.e. 2kg, but you have also concentrated all the kinetic energy into a small volume at the point of collision. So at the moment of collision we have everything at rest and a very high energy density. If you make the speeds of the 1kg masses high enough this will form a black hole.

I have to confess I don't know if this argument applies to light beams because unlike the masses a light beam has no rest frame. You cannot argue that the point in between two colliding light beams is a rest frame for the collision. However it seems plausible that by concentrating the light from multiple beams into a small volume you could create a black hole.

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  • $\begingroup$ Depends on your definition of a black hole. The matter might become incredibly dense like a black hole, but it would evaporate almost instantaneously. $\endgroup$ – Neil Jul 13 '16 at 11:30
  • $\begingroup$ @Neil: if you can make the colliding matter dense enough it would not evaporate because a horizon would form before it got a chance. $\endgroup$ – John Rennie Jul 13 '16 at 12:33
  • $\begingroup$ It is a pedantic point on my part, since we don't even know if such a thing is possible. The horizon would be too small to capture other atoms, but assuming it were, it would evaporate quickly thereafter. $\endgroup$ – Neil Jul 13 '16 at 12:54
  • $\begingroup$ Is it possible that the 1km ball has a size (a radius), and this radius is also reference dependent so that in any reference frame, the black hole condition can not be met? $\endgroup$ – XXDD Jul 19 '16 at 15:25

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