Explicit bilayered and thin-shell GR models show that relaxing monotonic density or isotropy lets compactness approach Bondi's bound or even the black hole limit.
Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps
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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.
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2024 1verdicts
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Beyond Buchdahl's limit: bilayered stars and thin-shell configurations
Explicit bilayered and thin-shell GR models show that relaxing monotonic density or isotropy lets compactness approach Bondi's bound or even the black hole limit.