The following question was answered and the answers do make it seem like photons with a high enough frequency, could, in theory, turn into black holes:

How much energy does a photon need to form a black hole?

Now, assuming these answers are correct, if an observer is accelerating towards a source of electromagnetic radiation of a particular frequency, there is going to be a blue shift and this means perceived frequency of the photons is going to change due to the relatavistic Doppler effect. Eventually the frequency would exceed the frequency calculated in the answers to the above question. Will the observer perceive the photons to have turned into black holes at that point?

I thought about this for a while and it seemed a little similar to the perceived Lorentz contraction of objects at relativistic speeds and an apparent possibility of the formation of black holes from such a contraction. However, this was answered in this question:

Can a black hole form due to Lorentz contraction?

It turns out that the formation of black holes is a function (a tensor) of not only the density but also other variables the changes in which cancel out the changes in perceived density as the speed increases. However, the answer makes use of the existence of a 'rest frame' of the 'test object' and unfortunately, for a photon there is really no rest frame. Which means there is a missing link in order for the answer to the Lorentz contraction question to be extrapolated to our current blue shift question.

  • $\begingroup$ If it is a photon, it must go with velocity c in all frames and it must be zero mass. Surprisingly some research is going on , see for example arxiv.org/abs/1611.03164 . It aint simple. $\endgroup$
    – anna v
    Mar 25 at 15:40
  • $\begingroup$ "assuming these answers are correct" - They are not. Relativistic objects, including photons, don't curve spacetime. See this: physics.stackexchange.com/questions/3436 $\endgroup$
    – safesphere
    Mar 26 at 12:58

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