Junction Conditions / Discontinuities in Solutions

1. Darmois G: Les Équations de la Gravitation Einsteinienne (Chapitre V), Mémorial de Sciences Mathématiques, Fascicule XXV, (Paris: Gauthier-Villars, 1927)
2. Lichnerowicz A: Théories Relativistes de la Gravitation et de l`Electromagnétisme, (Paris: Masson, 1955)
3. Dautcourt G: ..., Math. Nachr. 27 (1964), 277
4. Israel W: Singular Hypersurfaces and Thin Shells in General Relativity, Nuovo Cimento B 44 (1966), 1
   NB: No discussion of relation to Cauchy initial value problem. First occurrence of the "Codazzi" mis-spelling error.
5. Papapetrou A, A Hamoui: Couches Simples de Matière en Relativité Générale, Ann. Inst. Henri Poincaré 9 (1968), 179
6. Taub A H: Space-Times with Distribution Valued Curvature Tensors, J. Math. Phys. 21 (1980), 1423
   NB: Finite jumps in the first and second partial derivatives of the metric across a 3-surface. Provides a formalism in which the second Bianchi identities are satisfied in the sense of distributions.
7. Clarke C J S, T Dray: Junction Conditions for Null Hypersurfaces, Class. Quantum Grav. 4 (1987), 265
   NB: Finite jumps in the first and second partial derivatives of the metric across a 3-surface. No discussion of relation to Cauchy initial value problem.
8. Lake K: Some Notes on the Propagation of Discontinuities in Solutions to the Einstein Equations, Vth Brazilian School of Cosmology and Gravitation, Ed. M Novello, (Singapore: World Scientific, 1987), 1
9. Barrabès C: Singular Hypersurfaces in General Relativity: a Unified Description, Class. Quantum Grav. 6 (1989), 581
   NB: (- + + +). Finite jumps in the first and second partial derivatives of the metric across a 3-surface. No discussion of relation to Cauchy initial value problem.
10. Fayos F et al: Matching Of The Vaidya And Robertson-Walker Metric, Class. Quantum Grav. 8 (1991), 2057
    NB: Vaidya spacetime: analogue of LTB model with null dust ("pure radiation").
11. Mars M, J M M Senovilla: Geometry of General Hypersurfaces in Spacetime: Junction Conditions, Class. Quantum Grav. 10 (1993), 1865
12. Friedrich H, G Nagy: The Initial Boundary Value Problem for Einstein's Vacuum Field Equation, Commun. Math. Phys. 201 (1999), 619
    NB: Very technical. (+ - - -). Communicated by H Nicolai.
13. van Elst H, G F R Ellis, B G Schmidt: On the Propagation of Jump Discontinuities in Relativistic Cosmology, Preprint gr-qc/0007003, uct-cosmology-00/06, AEI-2000-039

Selected References
Last revision: Tue, 22-8-2000 (This page is under construction)