CHOPTUIK SPACETIME AS AN EIGENVALUE PROBLEM

By fine-tuning generic Cauchy data, critical phenomena have recently b een discovered in the black-hole/no-black-hole ''phase transition'' of various gravitating systems. For the spherisymmetric scalar field sys tem, we find the ''critical'' spacetime separating the two phases by d emanding discrete scale invariance, analyticity, and an additional ref lection-type symmetry. The resulting nonlinear hyperbolic boundary val ue problem, with the rescaling factor Delta as the eigenvalue, is solv ed numerically by relaxation. We find Delta = 3.4439 +/- 0.0004.