Choptuik Spacetime as an Eigenvalue Problem

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 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 as the eigenvalue, is solved numerically by relaxation. We find 0ex{0ex}=0ex{0ex}3. 44390. 0004.