The Choptuik spacetime as an eigenvalue problem
General Relativity and Quantum Cosmology
2009-10-28 v2
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.
Cite
@article{arxiv.gr-qc/9507054,
title = {The Choptuik spacetime as an eigenvalue problem},
author = {Carsten Gundlach},
journal= {arXiv preprint arXiv:gr-qc/9507054},
year = {2009}
}
Comments
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