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DISCONTINUITIES HI SPACETIME
DISCONTINUITIES IN GENERAL RELATIVITY
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adiabatic assumption admissible coordinate system arbitrary auxiliary equations bivector characteristic equation class Cr coefficients components continuity condition coordinate neighborhood coordinate transformation covariant derivatives Cr manifold define DEFINITION discontinuity hypersurface Einstein tensor electro-magnetic element empty space energy-momentum tensor equations of motion equations of scheme field equations fluid forming the scalar Gaussian coordinates Gaussian with respect geodesic Gg-coordinates Hadamard theorem hence hypotheses Inhomogeneous Maxwell equation Jump Levi-Civita connection Lichnerowicz system linking equation manifold function Maxwell stress tensor metric tensor natural coordinates normal hyperbolic metric null hypersurfaces obtain Ohm's law order partial derivatives orthogonal physical parameters piecewise of class Poynting vector principle of geodesics Proof propagation speed proper energy density scalar product second fundamental form second fundamental tensor smooth manifold space-like or time-like space-time spherical coordinates spherically symmetric structural decomposition sub-structure subset tangent vector tensor calculus theorem of Hadamard time-like hypersurface unit time-like weak shock zero