Schwarzschild and Birkhoff a la Weyl

American Journal of Physics

Volumn 73, Issue 3, 2005, Pages 261-264

  Deser, S ^a   Franklin, J ^b  

^a BRANDEIS UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 15544375486     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1830505     Document Type: Article

References (14)

1. H. Weyl, "Zur Gravitationstheorie," Ann. Phys. (Leipzig) 54, 117-145 (1917); and in Space-Time-Matter, translated by H. L. Brose (Methuen, London, 1922); See also J. Droste, "The field of a single centre in Einstein's theory of gravitation," Proc. R. Acad. Sci. Amsterdam XIX, 197-215 (1917); D. Hilbert, "Die Grundlagen der Physik. (Zweitte Mitteilung)," Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl. 53-76 (1917).
2. H. Weyl, "Zur Gravitationstheorie," Ann. Phys. (Leipzig) 54, 117-145 (1917); and in Space-Time-Matter, translated by H. L. Brose (Methuen, London, 1922); See also J. Droste, "The field of a single centre in Einstein's theory of gravitation," Proc. R. Acad. Sci. Amsterdam XIX, 197-215 (1917); D. Hilbert, "Die Grundlagen der Physik. (Zweitte Mitteilung)," Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl. 53-76 (1917).
3. H. Weyl, "Zur Gravitationstheorie," Ann. Phys. (Leipzig) 54, 117-145 (1917); and in Space-Time-Matter, translated by H. L. Brose (Methuen, London, 1922); See also J. Droste, "The field of a single centre in Einstein's theory of gravitation," Proc. R. Acad. Sci. Amsterdam XIX, 197-215 (1917); D. Hilbert, "Die Grundlagen der Physik. (Zweitte Mitteilung)," Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl. 53-76 (1917).
4. H. Weyl, "Zur Gravitationstheorie," Ann. Phys. (Leipzig) 54, 117-145 (1917); and in Space-Time-Matter, translated by H. L. Brose (Methuen, London, 1922); See also J. Droste, "The field of a single centre in Einstein's theory of gravitation," Proc. R. Acad. Sci. Amsterdam XIX, 197-215 (1917); D. Hilbert, "Die Grundlagen der Physik. (Zweitte Mitteilung)," Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl. 53-76 (1917).
5. R. S. Palais, "Principle of symmetric criticality," Commun. Math. Phys. 69, 19-30 (1979).
6. M. E. Fels and C. G. Torre, "The principle of symmetric criticality in general relativity," Class. Quantum Grav. 19, 641-676 (2002), gr-qc/ 0108033.
7. S. Deser and B. Tekin, "Shortcuts to high symmetry solutions in gravitational theories," Class. Quantum Grav. 20, 4877-4884 (2003), gr-qc/ 0306114.
8. The theorem was obtained independently by J. T. Jebsen, "'Úber die Allgemeinen Kugelsymmetrischen Lösungen der Einsteinschen Gravitation-sgleichungen im Vakuum," Ark. f Mat., Astron. och Fys. 15 (18), 9 pages (1921), J. Eisland, "The group of motions of an Einstein space," Trans. A.M.S. 27, 213-245 (1925), and W. Alexandrow, "'Úber den Kugelsymmetrischen Vakuumvorgang in der Einstenschen Gravitationstheorie," Ann. Phys. (Leipzig) 72, 141-152 (1923). Birkhoff's version is in Relativity and Modern Physics (Harvard University Press, Cambridge, 1923). A translation (with comments) of the Jebsen paper will appear in JGRG, Nov. 2004.
9. The theorem was obtained independently by J. T. Jebsen, "'Úber die Allgemeinen Kugelsymmetrischen Lösungen der Einsteinschen Gravitation-sgleichungen im Vakuum," Ark. f Mat., Astron. och Fys. 15 (18), 9 pages (1921), J. Eisland, "The group of motions of an Einstein space," Trans. A.M.S. 27, 213-245 (1925), and W. Alexandrow, "'Úber den Kugelsymmetrischen Vakuumvorgang in der Einstenschen Gravitationstheorie," Ann. Phys. (Leipzig) 72, 141-152 (1923). Birkhoff's version is in Relativity and Modern Physics (Harvard University Press, Cambridge, 1923). A translation (with comments) of the Jebsen paper will appear in JGRG, Nov. 2004.
10. The theorem was obtained independently by J. T. Jebsen, "'Úber die Allgemeinen Kugelsymmetrischen Lösungen der Einsteinschen Gravitation-sgleichungen im Vakuum," Ark. f Mat., Astron. och Fys. 15 (18), 9 pages (1921), J. Eisland, "The group of motions of an Einstein space," Trans. A.M.S. 27, 213-245 (1925), and W. Alexandrow, "'Úber den Kugelsymmetrischen Vakuumvorgang in der Einstenschen Gravitationstheorie," Ann. Phys. (Leipzig) 72, 141-152 (1923). Birkhoff's version is in Relativity and Modern Physics (Harvard University Press, Cambridge, 1923). A translation (with comments) of the Jebsen paper will appear in JGRG, Nov. 2004.
11. The theorem was obtained independently by J. T. Jebsen, "'Úber die Allgemeinen Kugelsymmetrischen Lösungen der Einsteinschen Gravitation-sgleichungen im Vakuum," Ark. f Mat., Astron. och Fys. 15 (18), 9 pages (1921), J. Eisland, "The group of motions of an Einstein space," Trans. A.M.S. 27, 213-245 (1925), and W. Alexandrow, "'Úber den Kugelsymmetrischen Vakuumvorgang in der Einstenschen Gravitationstheorie," Ann. Phys. (Leipzig) 72, 141-152 (1923). Birkhoff's version is in Relativity and Modern Physics (Harvard University Press, Cambridge, 1923). A translation (with comments) of the Jebsen paper will appear in JGRG, Nov. 2004.
12. The advantage of this method speaks for itself. For Maxwell four vector potentials, plus their 16 gradients and 40 second derivatives are reduced to just one component and its radial derivative. For gravity, the savings are even more dramatic: 10 metric components, their 40 first and 100 second derivatives are reduced to just two functions and their radial derivatives.
13. S. Deser, J. Franklin, and B. Tekin, "Shortcuts to spherically symmetric solutions: A cautionary note," Class. Quantum Grav. 21, 5295 (2004).
14. R. Arnowitt, S. Deser, and C. W. Misner, "The dynamics of general relativity," in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962). Reprinted as gr-qc/0405109.