Monotonic functions in Bianchi models: why they exist and how to find them
- Author(s)
- Johannes Markus Heinzle, Claes Uggla
- Abstract
All rigorous and detailed dynamical results in Bianchi cosmology rest upon the existence of a hierarchical structure of conserved quantities and monotonic functions. In this paper we uncover the underlying general mechanism and derive this hierarchical structure from the scale-automorphism group for an illustrative example, vacuum and diagonal class A perfect fluid models. First, kinematically, the scale-automorphism group leads to a reduced dynamical system that consists of a hierarchy of scale-automorphism invariant sets. Second, we show that, dynamically, the scale-automorphism group results in scale-automorphism invariant monotone functions and conserved quantities that restrict the flow of the reduced dynamical system.
- Organisation(s)
- Gravitational Physics
- External organisation(s)
- Karlstad University
- Journal
- Classical and Quantum Gravity
- Volume
- 27
- No. of pages
- 27
- ISSN
- 0264-9381
- DOI
- https://doi.org/10.1088/0264-9381/27/1/015009
- Publication date
- 2010
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103036 Theoretical physics, 103028 Theory of relativity, 103019 Mathematical physics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/monotonic-functions-in-bianchi-models-why-they-exist-and-how-to-find-them(a423a8dd-d213-43b2-bc2a-1ef6b3a356eb).html