The Patchwork Divergence Theorem

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Dray, Tevian; Hellaby, Charles;
(1994)
  • Related identifiers: doi: 10.1063/1.530719
  • Subject: General Relativity and Quantum Cosmology | Mathematics - Differential Geometry

The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem ap... View more
  • References (15)
    15 references, page 1 of 2

    [1] Charles Hellaby and Tevian Dray, Failure of Standard Conservation Laws at a Classical Change of Signature, Phys. Rev. D, (to appear).

    [2] Richard L. Bishop and Samuel I. Goldberg, Tensor Analysis on Manifolds, Dover Publications, New York, 1968 and 1980.

    [3] W. Israel, Singular Hypersurfaces and Thin Shells in General Relativity, Nuov. Cim. 44B, 1-14 (1966) and (partial) corrections in Nuov. Cim. 48B, 463 (1967).

    [4] C J S Clarke and Tevian Dray, Junction Conditions for Null Hypersurfaces, Class. Quant. Grav. 4, 265 (1987).

    [5] Tevian Dray and T. Padmanabhan, Conserved Quantities from Piecewise Killing Vectors, Gen. Rel. Grav. 21, 741 (1989).

    [6] Tevian Dray, Corinne A. Manogue, and Robin W. Tucker, Particle Production from Signature Change, Gen. Rel. Grav. 23, 967 (1991).

    [7] Tevian Dray, Corinne A. Manogue, and Robin W. Tucker, The Effect of Signature Change on Scalar Field Propagation, in preparation.

    [8] Tevian Dray, Corinne A. Manogue, and Robin W. Tucker, The Scalar Field Equation in the Presence of Signature Change, Phys. Rev. D48, 2587 (1993).

    [9] G Ellis, A Sumeruk, D Coule, C Hellaby, Change of Signature in Classical Relativity, Class. Quant. Grav. 9, 1535 (1992).

    [10] G F R Ellis, Covariant Change of Signature in Classical Relativity, Gen. Rel. Grav. 24, 1047 (1992).

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