Magnetized deformable media in general relativity
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 15 (1971) no. 4, pp. 275-302. 
@article{AIHPA_1971__15_4_275_0,
     author = {Maugin, G\'erard A.},
     title = {Magnetized deformable media in general relativity},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {275--302},
     publisher = {Gauthier-Villars},
     volume = {15},
     number = {4},
     year = {1971},
     mrnumber = {290744},
     zbl = {0234.73037},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1971__15_4_275_0/}
}
TY  - JOUR
AU  - Maugin, Gérard A.
TI  - Magnetized deformable media in general relativity
JO  - Annales de l'institut Henri Poincaré. Section A, Physique Théorique
PY  - 1971
SP  - 275
EP  - 302
VL  - 15
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1971__15_4_275_0/
LA  - en
ID  - AIHPA_1971__15_4_275_0
ER  - 
%0 Journal Article
%A Maugin, Gérard A.
%T Magnetized deformable media in general relativity
%J Annales de l'institut Henri Poincaré. Section A, Physique Théorique
%D 1971
%P 275-302
%V 15
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1971__15_4_275_0/
%G en
%F AIHPA_1971__15_4_275_0
Maugin, Gérard A. Magnetized deformable media in general relativity. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 15 (1971) no. 4, pp. 275-302. http://www.numdam.org/item/AIHPA_1971__15_4_275_0/

[1] M. Born, Physik Zeit., t. 12, 1911, p. 569-575. | JFM

[2] G. Herglotz, Ann. Phys. (Leipzig), t. 36, 1911, p. 493. | JFM

[3] G. Nordstrom, Physik Zeit., t. 12, 1911, p. 854-857. | JFM

[4] E. Noether, Ann. Phys. (Leipzig), t. 31, 1910, p. 919. | JFM

[5] A.H. Taub and G. Salzmann, Physical Review, t. 95, 1954, p. 1659-1669. | MR | Zbl

[6] R.A. Grot and A.C. Eringen, Int. J. Engng. Sci., t. 4, 1966, p. 611-670.

[7] L.D. Landau and E.M. Lifshitz, Fluid mechanics, Pergamon, Oxford, 1959, chapter XV. | MR

[8] C. Eckart, Physical Review, t. 5 , 1940, p. 919.

[9] C. Marle, Ann. Inst. Henri Poincaré (Paris), t. 10, 1969, p. 67-194. | MR

[10] A.H. Taub, Physical Review, t. 94, 1954, p. 1468-1470. | MR

[11] A. Lichnerowicz, Théories relativistes de la gravitation et l'électromagnétisme, Masson, édit., Paris, 1955. | Zbl

[12] A.H. Taub, Illinois J. of Math., t. 1, 1957, p. 370-388. | MR | Zbl

[13] Mau Quan Pham, Ann. Mat. Pura Appl., t. 38, series 4, 1955, p. 121. | MR | Zbl

[14] A.C. Eringen, in Proceedings of International Symposium, A critical review of the foundations of relativistic and classical thermodynamics, edited by E. B. Stuart, B. Gal-Or and A. J. Brainard, Mono Book, Baltimore, 1970.

[15] Mau Quan Pham, Arch. Rat. Mech. Anal., t. 1, 1957, p. 54-79; Ann. Inst. Henri Poincaré, t. 2, 1965, p. 151-165. | Numdam | MR | Zbl

[16] A. Lichnerowicz, Relativistic hydrodynamics and magnetohydrodynamics, Benjamin, N. Y., 1967. | Zbl

[17] F. Halbwachs, Théorie relativiste des fluides à spin, Gauthier-Villars, Paris, 1960. | MR

[18] L. Sedov, P. M. M., t. 29, 1965, p. 417; t. 32, 1968, p. 771. Soviet Physics Doklady, t. 10, 1966, n° 9.

[19] V.L. Berdichevskii, P. M. M., t. 30, 1966, p. 510-530.

[20] C.B. Rayner, Proc. Royal Soc. London, t. 272 A, 1963, p. 44-53. | Zbl

[21] J.L. Synge, Math. Zeitschrift, t. 72, 1959, p. 82-87. | MR | Zbl

[22] L. Bragg, Arch. Rat. Mech. Anal., t. 18, 1965, p. 127-166. | MR | Zbl

[23] A. Bressan, Ann. Mat. Pura Appl., t. 62, 1963, p. 99. | MR | Zbl

[24] H.G. Schöpf, Annalen der Physik, t. 12, 1963, p. 377-395. | MR | Zbl

[25] R.A. Grot, J. of Math. Physics, t. 11, 1970, p. 109-113.

[26] A. Bressan, Rend. del Sem. Mat. della Univ. di Padova, t. 34, 1964, p. 1-73. | Numdam | MR | Zbl

[27] G.A. Maugin, Ph. D. Dissertation, Princeton University, Depart. of A. M. S., April 1971.

[28] C.B. Kafadar and A.C. Eringen, Int. J. Engng. Sci., 1971 (to appear).

[29] R.A. Grot, Int. J. Engng. Sci., t. 6, 1968, p. 295-307.

[30] A. Bressan, Riv. Mat. Univ. Parma, t. 4, 1964, p. 23-40. | MR | Zbl

[31] M.A. Ruderman, « Solid stars », in Scientific American, Feb. 1971, p. 24-31; Journal de Physique, t. 30, suppl. n° 11-12, 1969, p. C3.153-C3.160.

[32] A.C. Eringen, Mechanics of continua, J. Wiley, N. Y., 1966. | Zbl

[33] L. Söderholm, Arch. Rat. Mech. Anal., t. 39, 1970, p. 89-107. | MR | Zbl

[34] N.F. Jordan and A.C. Eringen, Int. J. Engng. Sci., t. 2, 1964, p. 59-95. | MR | Zbl

[35] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. | MR | Zbl

[36] M. Bouix, Fonctions généralisées et distributions, Masson, édit., Paris, 1964. | MR | Zbl

[37] P. Weiss, Proc. Royal Soc. London, t. A 169, 1939, p. 119. | JFM

[38] M. Von Laue, Relativitätstheorie, Vieweg, Braunschweig, vol. 1, 1921, p. 248. | JFM

[39] L.D. Landau and E.M. Lifshitz, The classical theory of fields, Pergamon, Oxford, 1962. | MR | Zbl

[40] J. Weber, General relativity and gravitational waves, Interscience Publ., N. Y., 1961. | MR | Zbl

[41] M. Abraham, R. C. Circ. Mat. Palermo, t. 28, 1909, p. 1; t. 30, 1910, p. 33. | JFM

[42] H. Minkowski, Nach. Ges. Wiss. Göttingen, 1908, p. 53; Math. Ann., t. 68, 1910, p. 472. | JFM

[43] S.R. De Groot and L.G. Suttorp, Physica (Holland), t. 37, 1967, p. 284, 297; t. 39, 1968, p. 28, 41, 61, 77, 84.

[44] S. O'Brien and J.L. Synge, Communications of the Dublin Institute for advanced studies, sér. A, n° 9, 1953. | Zbl

[45] A.H. Taub, in Proceedings of first symposium of applied math., American Mathematical Soc., N. Y., 1949, p. 148-157. | Zbl

[46] R.C. Dixon and A.C. Eringen, Int. J. Engng. Sci., t. 3, 1965, p. 359-377. | MR

[47] For thie term, we need not consider the total variation as was pointed out by Taub, cf. Eq. (4.9) of Ref [12]

[48] (* d *) is the operator of codifferentiation; a star indicating that we take the dual of the quantity at its right, e. g., d *G = dĜ.