ANALYTIC APPROXIMATIONS TO THE SPACETIME OF A CRITICAL GRAVITATIONAL COLLAPSE

We present analytic expressions that approximate the behavior of the s pacetime of a collapsing spherically symmetric scalar field in the cri tical regime first discovered by Choptuik. We find that the critical r egion of spacetime can usefully be divided into a ''quiescent,'' an '' oscillatory,'' and a moving ''transition'' region; We find that in the quiescent and oscillatory regions the critical solution can be well a pproximated by a flat spacetime scalar field solution. A qualitative n onlinear matching of the solutions across the transition region yields the right order of magnitude for the oscillations of the discretely s elf-similar critical solution found by Choptuik.