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As far as I know, whenever we talk about a black hole, we refer to a static or stationary solution to Einstein field equations. I know the formation of a black hole can be discussed by the numerical GR, but I have never saw an analytical solution which can describe the formation of a black hole. So do anybody know that there actually exists such solution which has power to describe the formation of a black hole? Even the simplest case, for example, the spherical symmetric collapse of radiation into black hole can satisfy me very well.

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marked as duplicate by ACuriousMind, John Rennie black-holes Feb 20 '16 at 15:27

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  • $\begingroup$ I think there was one though I can't be sure. It describes a ring of radiation collapsing into a singularity. It was meant to demonstrate that the outside of this radiation ring was described by a Schwarzschild-like metric while the inside was simply flat space. $\endgroup$ – Horus Feb 20 '16 at 10:02
  • $\begingroup$ That would be very nice if there indeed exists such a solution. So you think such solution has already been used to explain the Birkhoff theorem? $\endgroup$ – Wein Eld Feb 20 '16 at 10:08
  • $\begingroup$ I don't think the theorem applies as notice I said Schwarzschild-like. A radiation ring is definitely not stationary or static. $\endgroup$ – Horus Feb 20 '16 at 10:20
  • $\begingroup$ I did a little check and there exist a class of solutions called pp-wave spacetimes. It concerns any form of massless radiation moving at the speed of light, I think you might find your answer somewhere there. $\endgroup$ – Horus Feb 20 '16 at 10:24
  • $\begingroup$ sciencedirect.com/science/article/pii/S0370269314005541 and links therein. Here is one I just found though not exactly what I described above, it does describe black hole formation. $\endgroup$ – Horus Feb 20 '16 at 10:33