Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps

Abstract

The goal of the present paper is three-fold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories. Second is to provide further analysis on the breakdown of hyperbolicity for the Skyrme model, sharpening the results of Crutchfield and Bell and comparing against a result of Gibbons, and provide a local well-posedness result for the dynamical problem in the Skyrme model. Third is to provide a short summary of the framework of regular hyperbolicity of Christodoulou for the relativity community. In the process, a general theorem about dominant energy conditions for Lagrangian theories of maps is proved, as well as several results concerning hyperbolicity of those maps.

Version 2: 26 pages. No figures. Subsumes the content previously announced in http://arxiv.org/abs/0909.4706 Small corrections + some additional remarks

Cited by in corpus (14)

• A Primer on Energy Conditions
• Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space
• Peculiar anisotropic stationary spherically symmetric solution of Einstein equations
• Relativistic Elasticity II
• Global existence of smooth solution to relativistic membrane equation with large data
• Spacetime diffeomorphisms as matter fields
• Global wellposedness of hedgehog solutions for the (3+1) Skyrme model
• Beyond Buchdahl's limit: bilayered stars and thin-shell configurations
• Inspecting Baby Skyrmions with Effective Metrics
• Nontrivial Causal Structures Engendered by Knotted Solitons
• Characteristic analysis for integrable soliton models on two-dimensional target spaces
• Relativistic elastic membranes: rotating disks and Dyson spheres
• From Hopf fibrations to exotic causal replacements
• On the geometrical hypotheses underlying wave functions and their emerging dynamics