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 ``scale-invariant'' part of the metric. The periodicity of the scale-invariant part implies periodic self-similarity of the spacetime. We also analyze a toy model that exhibits many of the features of Choptuik scaling.
Physical Review D
- Pub Date:
- September 1997
- Canonical formalism Lagrangians and variational principles;
- Einstein-Maxwell spacetimes spacetimes with fluids radiation or classical fields;
- General Relativity and Quantum Cosmology
- references added and discussion modified