Choptuik scaling and the scale invariance of Einstein's equation
Abstract
The relationship of Choptuik scaling to the scale invariance of Einstein's equation is explored. Ordinary dynamical systems often have limit cycles: periodic orbits that are the asymptotic limit of generic solutions. We show how to separate Einstein's equation into the dynamics of the overall scale and the dynamics of the ``scaleinvariant'' part of the metric. The periodicity of the scaleinvariant part implies periodic selfsimilarity of the spacetime. We also analyze a toy model that exhibits many of the features of Choptuik scaling.
 Publication:

Physical Review D
 Pub Date:
 September 1997
 DOI:
 10.1103/PhysRevD.56.R3169
 arXiv:
 arXiv:grqc/9612015
 Bibcode:
 1997PhRvD..56.3169G
 Keywords:

 04.20.Fy;
 04.40.Nr;
 Canonical formalism Lagrangians and variational principles;
 EinsteinMaxwell spacetimes spacetimes with fluids radiation or classical fields;
 General Relativity and Quantum Cosmology
 EPrint:
 references added and discussion modified