Generalized regularly discontinuous solutions of the Einstein equations

Abstract

The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value differential geometry framework on a hypersurface is introduced, and corresponding compatibility conditions are deduced. Examples of generalized boundary layers, gravitational shock waves and thin shells are studied.

26 pages.

References in corpus (2)

• Invariance of the distributional curvature of the cone under smooth diffeomorphisms
• On the extension of the concept of Thin Shells to The Einstein-Cartan Theory