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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.