PBS Space Time recently had a challenge question involving two different proposed solutions to saving the earth from being trapped inside a Kugelblitz. https://www.youtube.com/watch?v=v3hd3AI2CAA
They also released the solution video https://www.youtube.com/watch?v=q_oHv6HCMX4
The short of it: Aliens fire a spherical shell of photons that have a total mass energy sufficient to create a black hole with a Schwarzschild radius of 1 light second at the Earth. The people of earth can build a perfectly reflective barrier at a radius of 1/2 light seconds that can reflect all of the incoming light and are able to violate the conservation of momentum so that the barrier will not be imparted with all of that momentum that a reflective surface normally would be.
Will the earth be saved? Or will it still be trapped in this massive Kugelblitz?
The answer provided by the solution video is that this disco ball solution will not work because the event horizon would still form once the light shell reached a radius of 1 light second. But I'm unconvinced that the disco ball wouldn't work. I feel like the reasoning around it doesn't take into account that changes in spacetime geometry only propagate at the speed of light.
While all of the energy is at the distance of the alien ships before they fire, it's not concentrated enough to make a black hole yet. And then for all incident photons on their entire journey inward to the disco ball, the space that they are traveling through is only warped to the exact same extent as it was at the beginning of their journey (which is to say not at all except for whatever warping occurs normally outside of this wacky scenario).
On their return trip back out they immediately run into warped space caused by some cone of the other nearby photons whose effects of their inward trip has had time to reach the space that the photon is now traveling through, but it's not the full effect because the effects of nearly 3/4 of the sphere still hasn't reached the space the photon is traveling through on it's return trip. It seems to me that the event horizon would not form because there isn't enough time for all the gravity waves to propagate to all parts of the 1/2 light second radius sphere.
Now, I believe there is some radius at which if you built your disco ball, enough of the effects would have had time to propagate to to form a black hole anyway, but I'm not at all sure how to calculate that. But I feel like you'd need to calculate that radius to be sure 1/2 light second is inside it.
Am I wrong about this? Would the disco ball really not work at any radius less than 1 light second? Or are they just ignoring the finite speeds of gravity waves in their explanation and Penrose diagram?