Abstract
For a thin shell, the intrinsic 3-pressure will be shown to be analogous to -A, whereA is the classical surface tension: First, interior and exterior Schwarzschild solutions will be matched together such that the surface layer generated at the common boundary has no gravitational mass; then its intrinsic 3-pressure represents a surface tension fulfilling Kelvin's relation between mean curvature and pressure difference in the Newtonian limit. Second, after a suitable definition of mean curvature, the general relativistic analog to Kelvin's relation will be proven to be contained in the equation of motion of the surface layer.
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References
Lanczos, K. (1924).Ann. Phys. (Leipzig),74(4), 518.
Papapetrou, A., and Treder, H. (1959).Math. Nachr.,20, 53.
Dautcourt, G. (1963/64).Math. Nachr.,27, 277.
Israel, W. (1966).Nuovo Cimento B,44, 1.
Papapetrou, A., and Hamoui, A. (1968).Ann. Inst. H. Poincare,A9, 179.
Kuhař, K. (1968).Czech. J. Phys.,B18, 435.
Boulware, D. (1973).Phys. Rev. D,8, 2363.
Denisov, V. I. (1972).J. Exp. Teor. Phys.,62, 1990 [Engl. transi. (1972)Sov. Phys. JETP,35, 1038.
Lake, K. (1981).Lett. Nuovo Cim. ser. 2,30, 186.
Schmidt, H. J. (1983). Contributed Papers, GR10, Padova, 4–9 July 1983, Vol. 1, B. Bertofti, ed. p. 339.
Urbandtke, H. (1912).Acta Physica Austriaca,35, 1.
Frehland, E. (1912).Ann. Phys. (Leipzig),28(7), 91.
Lake, K. (1979).Phys. Rev. D,19, 2847.
Morgan, L., and Morgan, T. (1970).Phys. Rev. D,2, 2756.
Voorhees, B. (1972).Phys. Rev. D,5, 2413.
Einstein, A. (1939).Ann. Math.,40, 922.
Gottlöber, S. (1980).Diss. A, Akad. Wiss. Berlin.
Israel, W., and Stewart, J. (1980).Gen. Rel. Grav. II, A. Held, ed. (Plenum, New York), p. 491.
Neugebauer, G. (1980).Relativistische Thermodynamik (Akademierverlag, Berlin).
Ono, S., and Kondo, S. (1960).Handbuch der Physik, Vol. 10, S. Flügge, ed. (Springer Verlag, Berlin), p. 134.
López, C. (1981).Nuovo Cimento B,66, 17.
Krasilnikov, V. A., and Pavlov, V. I. (1972).Vestn. Univ. Moskau (III),27, 235.
Thomson, W. (Lord Kelvin) (1858).Proc. R. Soc. London,9, 255.
Taub, A. (1980).J. Math. Phys.,21, 1423.
Cohen, M., and Cohen, J. (1971).Relativity and Gravitation, C. Kuper, ed. (Gordon/Breach, New York), p. 99.
Maeda, K., and Sato, H. (1983).Progr. Theor. Phys.,70, 772.
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Schmidt, H.J. Surface layers in general relativity and their relation to surface tensions. Gen Relat Gravit 16, 1053–1061 (1984). https://doi.org/10.1007/BF00760644
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DOI: https://doi.org/10.1007/BF00760644