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Maxwell’s equations in the Debye potential formalism. (English) Zbl 0589.53070

Based on a geometrically biased generalization to curved space-times of the potential current formalism of Laporte and Uhlenbeck, this work proposes a procedure for introducing electromagnetic field sources into the Debye or two-component Herz potential formalism. This formalism has been shown to extend to all curved space-times. An explicit application to the Schwarzschild case.
Reviewer: S.I.Anderson

MSC:

53B50 Applications of local differential geometry to the sciences
83C50 Electromagnetic fields in general relativity and gravitational theory
78A25 Electromagnetic theory (general)
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References:

[1] J.M. Cohen and L.S. Kegeles , Phys. Rev. D. , t. 10 , 1974 , p. 1070 . MR 406332
[2] O. Laporte and G.E. Uhlenbeck , Phys. Rev. , t. 37 , 1931 , p. 1380 . Zbl 0002.09001 | JFM 57.1216.01 · Zbl 0002.09001 · doi:10.1103/PhysRev.37.1380
[3] A. Nisbet , Proc. Roy. Soc. , t. A 231 , 1955 , p. 250 . MR 83361 | Zbl 0065.42007 · Zbl 0065.42007 · doi:10.1098/rspa.1955.0170
[4] H. Stephani , J. Math. Phys. , t. 15 , 1974 , p. 14 .
[5] H. Flanders , Differential forms , Academic Press , New York , London , 1963 . MR 162198 | Zbl 0112.32003 · Zbl 0112.32003
[6] C. Godbillon , Géométrie différentielle et mécanique analytique , Herman , Paris , 1969 . MR 242081 | Zbl 0174.24602 · Zbl 0174.24602
[7] Choquet-Bruat et al., Analysis, manifolds and Physics , North Holland Publishing Co. , Amsterdam , New York , Oxford . Zbl 0385.58001 · Zbl 0385.58001
[8] Newman and Penrose , J. Math. Phys. , t. 3 , 1952 , p. 566 . Zbl 0108.40905 · Zbl 0108.40905 · doi:10.1063/1.1724257
[9] D. Kramer et al., Exact solutions of Einstein’s field equations , VEB Deutscher Verlag der Wissenschaften , Berlin , 1980 . Zbl 0449.53018 · Zbl 0449.53018
[10] J.N. Goldberg et al., J. Math. Phys. , t. 8 , 1967 , p. 2155 . Zbl 0155.57402 · Zbl 0155.57402 · doi:10.1063/1.1705135
[11] E. Newman and R. Penrose , J. Math. Phys. , t. 7 , 1966 , p. 863 .
[12] T. Elster , Astrophys . Space Sci. , t. 71 , 1980 , p. 171 . MR 579655
[13] B. Mashoon , Phys. Rev. D. , t. 7 , 1973 , p. 2807 .
[14] R. Fabri , Phys. Rev. D. , t. 12 , 1975 , p. 933 .
[15] R.A. Breuer et al., Phys. Rev. D , 8 , 1973 , p. 4309 .
[16] R.F. Arenstorf et al., J. Math. Phys. , t. 19 , 1978 , p. 833 . MR 488112
[17] K.R. Pechenick et al., Il Nuovo Cimento , t. 64B 2, 1981 , p. 453 .
[18] D.R. Brill and J.M. Cohen , Phys. Rev. , t. 143 , 1966 , p. 1011 . MR 198929
[19] J.M. Cohen , J. Math. Phys. , t. 8 , 1967 , p. 1477 .
[20] S. Teukolsky , Ap. J. , t. 185 , p. 635 .
[21] E.P. Fackerell and J.R. Ipser , Phys. Rev. D , t. 5 , 1972 , p. 2455 .
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