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Consider a lone photon. As its frequency increases, its energy increases. Taken to the limit, a sufficiently-high-frequency photon could be a black hole unto itself.

But the frequency of a photon is dependent on the inertial frame of the observer. Two observers could each observe this photon to be either above or below this critical frequency. Or, I could accelerate to "catch up" to this photon, red-shifting it until it is no longer energetic enough to be a black hole.

So couldn't I at one moment observe a particle to disappear beyond the event horizon, accelerate until the event horizon no longer exists, and hence observe what happened to the particle after crossing that threshold?

Is this in-principle possible? If not, why not?

EDIT: to clarify, I am not asking how much energy-due-to-photon-momentum is required to create a black hole, I am asking: given that threshold energy, how does the event horizon appear to different inertial frames which observe the photon to be above/below this threshold?

spraff
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    Possible duplicate of How much energy does a photon need to form a black hole? – Bosoneando Jul 24 '16 at 14:24
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    It cannot happen that one inertial frame sees a horizon but another doesn't, cf. http://physics.stackexchange.com/q/3436/50583. That this case is a photon whose energy changes and not a mass whose velocity changes appears to be irrelevanat to me. – ACuriousMind Jul 24 '16 at 14:31
  • The Special Relativity works quite differently (and much more complicated) in the case of the elemental particles. How the GR works in their case, nobody knows. I don't think that an enough energetic photon would be a black hole, instead some quantum gravity effect will appear (similarly, as I think there is no singularity [i.e. point-like mass with infinite density] in the centre of a black hole). Now the problem is that the experimental physics would require $10^{15}$ times stronger accelerators to measure them. – peterh Jul 24 '16 at 15:58
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    related: http://physics.stackexchange.com/questions/3436/if-a-1kg-mass-was-accelerated-close-to-the-speed-of-light-would-it-turn-into-a-b?noredirect=1&lq=1 – Larry Harson Jul 24 '16 at 21:53
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    "Taken to the limit, a sufficiently-high-frequency photon could be a black hole unto itself." - a black hole has a rest mass and thus cannot have speed $c$ in any inertial reference frame. A photon has speed $c$ in all inertial reference frames. – Alfred Centauri Jul 24 '16 at 22:02
  • Why must a black hole have a rest mass? The premise of my question is that it might not. 2) So a photon can increase the gravitational field arbitrarily without creating a black hole, right? Your answer might be a logical argument but it suggests no reason why such an object can't be created.
    • – spraff Jul 24 '16 at 22:10
  • In GR the nearest thing to a photon would be a light pulse/wavepacket, and the gravitational field of a light pulse doesn't look anything like that of a massive particle. Although this is a weak field calculation (I don't know of a full calculation) it's far from obvious that a light pulse could form a black hole. I suspect your question is based upon a false assumption. – John Rennie Jul 25 '16 at 09:38
  • PS I agree your question isn't a duplicate and shouldn't be closed – John Rennie Jul 25 '16 at 09:38