The Choptuik spacetime as an eigenvalue problem

Abstract

By fine-tuning generic Cauchy data, critical phenomena have recently been discovered in the black hole/no black hole "phase transition" of various gravitating systems. For the spherisymmetric real scalar field system, we find the "critical" spacetime separating the two phases by demanding discrete scale-invariance, analyticity, and an additional reflection-type symmetry. The resulting nonlinear hyperbolic boundary value problem, with the rescaling factor Delta as the eigenvalue, is solved numerically by relaxation. We find Delta = 3.4439 +/- 0.0004.

Review section rewritten; sign error in equation (4), error concerning non-minimally coupled scalar field, one typo in table corrected, references added. To be published in Phys. Rev. Lett

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