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

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

2010-11-12

arxiv.org/abs/1011.3029v2

Class.Quant.Grav.28:215008,2011

Physics

Mathematical Physics

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

Scientific paper

10.1088/0264-9381/28/21/215008

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.

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