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Good_Burning_Plastic comments on Stupid Questions, December 2015 - Less Wrong Discussion
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Why don't ordinary photons spontaneously collapse into black holes? You should get a singularity if the energy density in any region of space is high enough. But you can pick an inertial reference frame such that any given photon has arbitrarily high frequency (and thus energy) due to blueshift. Since any inertial reference frame is as valid as any other due to relativity, why don't all photons collapse under their own weight?
That applies to anything, not just photons. In any event, I'm not an expert in general relativity, but I think what matters is the energy of an object in its own center-of-mass frame (a.k.a. its mass). (And a single photon, or a collection of photons traveling in the same direction, doesn't even have a center-of-mass frame.) Anyway, elementary particles (including photons) already are point-like so far as we know, so they couldn't possibly collapse any further.