Singular hypersurfaces and thin shells in general relativity
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J. R. Oppenheimer andH. Snyder:Phys. Rev.,56, 455 (1939);F. Hoyle andJ. V. Narlikar:Proc. Roy. Soc., A278, 465 (1964);C. W. Misner andD.H. Sharp:Phys. Rev.,136, B 571 (1964);G. C. McVittie:Astrophys. Journ.,140, 409 (1964);H. Nariai andK. Tomita:Progr. Theor. Phys.,34, 155 (1965).
C. Lanczos:Phys. Zeits.,23, 539 (1922);Ann. der Phys.,74, 518 (1924). See alsoN. Sen:Ann. der Phys.,73, 365 (1924).
Boundary surfaces:A. H. Taub:Ill. Journ. Math.,1, 370 (1957);N. Coburn:Journ. Math. and Mech.,10, 361 (1961);R. Abraham:Journ. Math. and Mech.,11, 553 (1962);D. G. B. Edelen andT. Y. Thomas:Journ. Math. Anal. Appl.,7, 247 (1963);G. Dautcourt:Arch. Rat. Mech. and Anal.,13, 55 (1963);H. Nariai:Progr. Theor. Phys.,34, 173 (1965). Surface layers:G. Dautcourt:Math. Nachr.,27, 277 (1964). This reference also treatsnull surface layers (e.g. shells of photons), an important topic which lies outside the scope of the present work.
A. Lichnerowicz:Théories Relativistes de la Gravitation et de l’Electromagnétisme (Paris, 1955). Also:J. L. Synge:Relativity: The General Theory (Amsterdam, 1960), p. 39;W. Israel:Proc. Roy. Soc., A248, 404 (1958).
S. O’Brien andJ. L. Synge:Commun. Dublin Inst. Adv. Stud., A, No. 9 (1952). See alsoLanczos, ref. (2).
Cf.R. K. Sachs: inRelativity, Groups, Topology, edited byde Witt andde Witt (New York, 1964), p. 534.
H. P. Robertson:Proc. Edinburgh Math. Soc.,5, 63 (1937);L. Infeld andA. Schild:Rev. Mod. Phys.,21, 408 (1949);A. H. Taub:Journ. Math. Phys.,5, 112 (1964).
H. Weyl:Raum, Zeit, Materie, 5th edition, Sect.36 (Berlin, 1923);L. Infeld andJ. Plebanski:Motion and Relativity, Sect.I-6, (New York, 1960);W. B. Bonnor andN. S. Swaminarayan:Zeits. Phys.,177, 240 (1964). For critical comments, seeM. Carmeli:Phys. Lett.,11, 24 (1964).
Seee.g. J. L. Synge:Relativity: The General Theory (Amsterdam, 1960), p. 175.
Throughout the paper Greek indices take the range 1–4, Latin indices the range 2, 3, 4.
See ref. (9), p. 35.
See ref. (9), p. 276.
W. Israel:Gravitational Collapse of a Spherical Shell and the Problem of Causality, Preprint Series A, No. 45, Mathematics Department, University of Alberta. (October 1965).