Nonsmooth mechanics for general relativity
Description
Title: Nonsmooth mechanics for general relativity
Author: Ding Jia
Abstract: We study relativistic matter and gravitational fields subject to inequality constraints. Conditions are derived for solutions to the action principle as local extrema of the action. In regions where constraints remain inactive, the fields satisfy the standard Euler-Lagrange equations. On hypersurfaces where constraints are activated, field derivatives can jump discontinuously in order to obey the constraints. For matter fields, energy-momentum flux is conserved across the hypersurfaces. For gravitational fields, boundary terms in the action that cancel in smooth mechanics are not guaranteed to canceled across the hypersurface. The resulting theory allows solutions to extend beyond gravitational singularities.
Version history
- Original versions: Article v1.0
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