Summary
In the last thirty years a relativistic kinetic theory of transport processes has been developed, which is based on an appropriate generalization of Boltzmann’s celebrated equation. The relevant macroscopic laws could be derived in the framework of this theory. Moreover transport coefficients could be calculated, according to various procedures:
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(a)
the eigenvalue method,
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(b)
the simplified collision description,
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(c)
the moment method and
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(d)
the orthogonal functions method.
The last — new — method is free from the limitations, inherent in the first three. In fact it allows to find values for the relativistic transport coefficients of systems of particles with arbitrary cross-sections in successive approximations Results are presented for the heat conductivity, the viscosities and the coefficient of sound absorption of simple relativistic gases with different cross-sections, in various approximations.
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References
A. Lichnerowicz and R. Marrot, Compt. Rend. Acad. Sc., Paris 210 (1940) 759; 211 (1940) 177; 219 (1944) 270.
R. Marrot, Journ. Math. pures et appliquées 25 (1946) 12.
N.A. Chernikov, Sov. Phys. Doklady 2 (1957) 103, 248; 5 (1960) 764; Naukn. Dokl. Vyssh. Shkoly, Ser. Fiz.-Mat. 1 (1959) 168.
G.E. Tauber and J.W. Weinberg, Phys. Rev. 122 (1961) 1342.
W. Israel, J. Math. Phys. 4 (1963) 1163.
R. Hakim, J. Math. Phys. 8 (1967) 1315, Phys. Rev. 162 (1967) 128.
N.G. van Kampen, Physica 43 (1969) 244.
Ch.G. van Weert, Proc. Kon. Ned. Akad. Wet., Amsterdam B 73 (1970) 381, 397, 500, 517 (thesis Amsterdam).
S.R. de Groot and L.G. Suttorp, Foundations of electrodynamics (North-Holland) Amsterdam, 1972 (chapter V, section 2a).
W.A. van Leeuwen, Proc. Kon. Ned. Akad. Wet., Amsterdam B 74 (1971) 122, 134, 150, 269, 276 (thesis Amsterdam).
S.R. de Groot, Ch.G. van Weert, W.Th. Hermens and W.A. van Leeuwen, Physica 40 (1968–1969) 257, 581; 42 (1969) 309; Phys. Lett. 26A (1968) 345, 439.
E.C.G. Stueckelberg, Helv. Phys. Acta 25 (1952) 577.
W. Iieitler, Ann. Inst. Henri Poincaré 15 (1967) 67.
F. Jüttner, Ann. Physik 34 (1911) 856.
C. Eckart, Phys. Rev. 58 (1940) 919.
G.A. Kluitenberg, S.R. de Groot and P. Mazur, Physica 19 (1953) 689, 1079; 20 (1954) 199; 21 (1955) 148.
W.Th. Iiermens, Proc. Kon. Ned. Akad. Wet., Amsterdam B 74 (1971) 376, 387, 461, 478 (thesis Amsterdam).
W. Th. Hermens, W.A. van Leeuwen, Ch.G. van Weert and S.R. de Groot, Physica 60 (1972) 472
P. Curie, Oeuvres, p. 118, Paris, 1908.
S.R. de Groot and P. Mazur, Non-equilibrium thermodynamics (North-Holland) Amsterdam, 1962.
L. Onsager, Phys. Rev. 37 (1931) 405; 38 (1931) 2265.
H.B.G. Casimir, Rev. Mod. Phys. 17 (1945) 343.
J. Bernstein, G. Feinberg and T.D. Lee, Phys. Rev. 139B (1965) 1650.
C.S. Wang (Chang) and G.E. Uhlenbeck, Rep. M 999, Eng. Res. Inst., Univ. of Michigan, 1952.
L. Waldmann, Z. Naturf. 11A (1956) 523; Encycl. Phys. 12 (1958) 370.
W.A. van Leeuwen and S.R. de Groot, Physica 51 (1971) 1, 16, 32.
E. Gross, D. Bhatnager and M. Krook, Phys. Rev. 94, (1954) 511.
C. Marle, Ann. Inst. Henri Poincaré 10 (1969) 67, 127.
H. Grad, Comm. Pure Appl. Math. 2 (1949) 331; Phys. Fluids 6 (1963) 147
W. Israel and J.N. Vardalas, Lett. N. Cim. 4 (1970) 887.
B. Vignon, Ann. Inst. Henri Poincaré 10 (1969) 31.
J.L. Anderson, Proc. 1969 Relativity conference in the Mid-West (Plenum) New York, 1970.
J.M. Stewart, Non-equilibrium relativistic kinetic theory ( Springer ), Berlin-Heidelberg-New York, 1971.
C.W. Misner, Astrophys. J. 151 (1968) 431.
S. Chapman, Phil. Trans. Roy. Soc. A 216 (1916) 279; A 217 (1917) 115.
D. Enskog, Dissertation, Uppsala, 1917.
W.A. van Leeuwen, P.H. Polak and S.R. de Groot, Phys. Lett. 37A (1971) 323; C.R. Acad. Sc., Paris 274 (1972) 431; Physica, to be published.
D.C. Kelly, Unpublished report, Miami University, Oxford, Ohio, 1963. A different set of orthogonal functions was proposed here, but since it is incomplete, no method could be developed from it.
S. Chapman and T.G. Cowling, The mathematical theory of non-uniform gases, Cambridge University Press, 1939 (third edition, 1970 ).
J. Guichelaar, W.A. van Leeuwen and S.R. de Groot, Physica 59 (1972) 97.
S. Weinberg, Astrophys. J. 168 (1971) 175.
T.D. Lee, Astrophys. J. 111 (1950) 625.
M. Ruderman, Rep. Progr. Phys., 28 (1965) 411.
M. Ruderman,, Acc. Naz. Lincei 368 (1971) 1.
T. de Graaf, Acc. Naz. Lincei 368 (1971) 81.
J. Ehlers, Rendiconti Scuola Int. di Fisica “Enrico Fermi” 47 (1971) 1.
W. Israel, in General Relativity, Papers in honour of J.L. Synge (Clarendon Press) Oxford, 1972.
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de Groot, S.R. (1973). Relativistic Boltzmann Theory. In: Cohen, E.G.D., Thirring, W. (eds) The Boltzmann Equation. Acta Physica Austriaca, vol 10/1973. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8336-6_21
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