Black holes have rest mass, made of light or not, so this is impossible. Can you spot the error?
It is true that black holes have rest mass, regardless of the form of mass-energy used to create them. As such it is impossible for them to travel at the speed of light. However the error-hint you give is misleading.
one photon has no rest mass, while a bunch of photons in a box (photon gas) does.
This is true but innaplicable. Making a black hole out of photons requires that the photons are not all moving in the same direction. For an explanation see here. Alternately, simply consider the case where all the energy is concentrated into a single (ridiculously) high energy photon. As you observe, “one photon has no rest mass”. No black hole is formed by a single (unconfined) photon. The explanation is somewhat similar to why you don’t form a black hole if you travel really fast.
It is true that black holes have rest mass, regardless of the form of mass-energy used to create them. As such it is impossible for them to travel at the speed of light. However the error-hint you give is misleading.
This is true but innaplicable. Making a black hole out of photons requires that the photons are not all moving in the same direction. For an explanation see here. Alternately, simply consider the case where all the energy is concentrated into a single (ridiculously) high energy photon. As you observe, “one photon has no rest mass”. No black hole is formed by a single (unconfined) photon. The explanation is somewhat similar to why you don’t form a black hole if you travel really fast.