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If you can make black holes out of light you can make black holes out of light that is emmited from the moving frame and concentrated into one spot and that would not have enough energy to form a black hole in the moving frame but because of the blueshift it would have enough energy to form a black hole in the stationary frame. What is the cause of this effect in the moving frame?

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Whether a black hole will form or not depends on the value of an object called the stress-energy tensor. This is usually written as a four by four matrix, and the energy density is only one value inside this matrix. The other values tell you about the momentum and pressure. When you blueshift the light you change the energy density, but you also change the momentum because $p = h/\lambda$ and the change in momentum balances out the change in energy density so a black hole cannot form.

The black holes formed from light require two or more light beams travelling in different directions. Then the momenta of the light beams can cancel to make the total momentum zero and leave just the energy density and this can form a black hole. Specifically it can form a type of black hole called a kugelblitz.

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  • $\begingroup$ "the change in momentum balances out the change in energy density" - Correct, kinetic energy does not curve spacetime, because its contribution is exactly canceled out by the opposite contribution of momentum (gravitomagnetism). So two relativistic bullets (including photons) passing by each other and each producing a zero curvature would not even feel each other, much less create a black hole. The fact that the total momentum of the system is zero does not logically imply that gravitomagnetism contributions of two objects cancel each other. There will be only very small non-linear effects. $\endgroup$
    – safesphere
    Commented May 24, 2021 at 19:38