Elliptic functions in spherically symmetric solutions of Einstein's equations

G. C. McVittie

Annales de l'I.H.P. Physique théorique (1984)

  • Volume: 40, Issue: 3, page 235-271
  • ISSN: 0246-0211

How to cite

top

McVittie, G. C.. "Elliptic functions in spherically symmetric solutions of Einstein's equations." Annales de l'I.H.P. Physique théorique 40.3 (1984): 235-271. <http://eudml.org/doc/76236>.

@article{McVittie1984,
author = {McVittie, G. C.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Robinson-Walken universes; Einstein's equations; elliptic functions},
language = {eng},
number = {3},
pages = {235-271},
publisher = {Gauthier-Villars},
title = {Elliptic functions in spherically symmetric solutions of Einstein's equations},
url = {http://eudml.org/doc/76236},
volume = {40},
year = {1984},
}

TY - JOUR
AU - McVittie, G. C.
TI - Elliptic functions in spherically symmetric solutions of Einstein's equations
JO - Annales de l'I.H.P. Physique théorique
PY - 1984
PB - Gauthier-Villars
VL - 40
IS - 3
SP - 235
EP - 271
LA - eng
KW - Robinson-Walken universes; Einstein's equations; elliptic functions
UR - http://eudml.org/doc/76236
ER -

References

top
  1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972, Sec. 18. Zbl0543.33001
  2. A. Banerjee and S. Banerji, Acta Phys. Polonica, t. B7, 1976, p. 389. 
  3. H. Bondi, Mon. Not. R. astr. Soc., t. 142, 1969, p. 333. Zbl0165.29401
  4. W.B. Bonnor and M.C. Faulkes, Mon. Not. R. astr. Soc., t. 137, 1967, p. 239. 
  5. N. Chakravarty, S.B.D. Choudhury and A. Banerjee, Aust. J. Phys., t. 29, 1976, p. 113. 
  6. P.A.M. Dirac, Proc. R. Soc. Lond., A365, 1979, p. 19. See also in On the Path of Albert Einstein, Eds. B. Kursunoglu, A. Perlmutter, L. F. Scott., Plenum Press, New York, 1979, p. 1-13. 
  7. M.C. Faulkes, Prog. Theor. Phys., t. 42, 1969, p. 1139. MR250642
  8. E.N. Glass, J. Math. Phys., t. 20, 1979, p. 1508. 
  9. E.N. Glass and B. Mashhoon, Astrophys. J., t. 205, 1976, p. 570. 
  10. E.L. Ince, Ordinary Differential Equations, Dover, 1956 (a) Sec. 14.314, Sub-case i(d), items 1° and 3° ; (b) Sec. 14.314, Sub-case i(d), item 5°(β); (c) p. 87. MR10757
  11. E. Kamke, Differential-gleichungen: Losungsmethoden und Losungen, Chelsea, 1971, New York, p. 548-549. 
  12. H. Knutsen and R. Stabell, Ann. Inst. Henri Poincaré, t. 31, 1979, p. 339. Eqs. (27) and (30). MR574138
  13. D. Kramer, H. Stephani, M. Maccallum, E. Herlt, Exact Solutions of Einstein's Field Equations. VEB Deut. Verlag der Wiss., Berlin, 1980. Camb. Univ. Press, p. 167-168. Zbl0449.53018
  14. P. Kustaanheimo and B. Qvist, Comment. Phys. Math. Helsingf., t. 13, 1948, p. 12. MR29304
  15. G.C. Mcvittie, Mon. Not. R. astr. Soc., t. 93, 1933, p. 325 (McV33). Zbl0007.08404JFM59.1520.02
  16. G.C. Mcvittie, Astrophys. J., t. 143, 1966, p. 682 (McV66). 
  17. G.C. Mcvittie, Ann. Inst. Henri Poincaré, t. 6, 1967, p. 1 (McV67). 
  18. G.C. Mcvittie, Comm. Roy. Soc. Edin. (Phys. Sci.), n° 16, 1979. 
  19. G.C. Mcvittie and R. Stabell, Ann. Inst. Henri Poincaré, t. 7, 1967, p. 103. Eqs. (19) and (20). Zbl0158.46503
  20. G.C. Mcvittie and R. Stabell, Ann. Inst. Henri Poincaré, t. 9, 1968, p. 371. 
  21. H. Nariai, Prog. Theor. Phys., t. 38, 1967, p. 92 and 740. 
  22. A.K. Raychaudhuri, Theoretical Cosmology. Clarendon Press, Oxford, 1979, p. 96-97. Zbl0443.53048
  23. I.H. Thompson and G.J. Whitrow, Mon. Not. R. astr. Soc., t. 136, 1967-1968, p. 207 and t. 139, p. 499. Zbl0162.59401
  24. E.T. Whittaker and G.N. Watson, A course of Modern Analysis. 3rd Ed. Camb. Univ. Press, 1920, Sec. 20.31. Zbl45.0433.02MR1424469

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.