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We present analytic expressions that approximate the behavior of the spacetime of a collapsing spherically symmetric scalar field in the critical regime first discovered by Choptuik. We find that the critical region 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 approximated by a flat spacetime scalar field solution. A qualitative nonlinear matching of the solutions across the transition region yields the right order of magnitude for the oscillations of the discretely self-similar critical solution found by Choptuik. © 1996 The American Physical Society.

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Physical Review D - Particles, Fields, Gravitation and Cosmology

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