Class of exact solutions in 5D gravity and its physical properties

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 53, Issue 2, 1996, Pages 731-737

  Billyard, Andrew ^a   Wesson, Paul S ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001638450     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.53.731     Document Type: Article

References (31)

1. P. S. Wesson and J. Ponce de Leon, J. Math. Phys. 33, 3883 (1992).
2. S. Rippl, C. Romero and R. Tavakol, Class. Quantum Grav. 12, 2411 (1995).
3. C. Romero, R. Tavakol, and R. Zalaletdinov, Queen Mary College, London, report, 1995 (unpublished).
4. D. Kalligas, P. S. Wesson, and C.W. F. Everitt, Astrophys. J. 439, 548 (1995).
5. R. D. Sorkin, Phys. Rev. Lett. 51, 87 (1983).
6. D. J. Gross and M. J. Perry, Nucl. Phys. B226, 29 (1983).
7. A. Davidson and D. Owen, Phys. Lett. 155B, 247 (1985).
8. P. S. Wesson, Phys. Lett. B 276, 299 (1992).
9. C. M. Will, Int. J. Mod. Phys. D 1, 13 (1992).
10. H. Liu and P. S. Wesson, University of Waterloo report (unpublished).
11. B. Mashhoon, H. Liu and P. S. Wesson, Phys. Lett. B 331, 305 (1994).
12. H. Liu and B. Mashhoon, Ann. Phys. (Leipzig) (to be published).
13. T. Kaluza, Sitz. Preuss. Akad. Wiss. 33, 966 (1921).
14. O. Klein, Z. Phys. 37, 895 (1926).
15. O. Klein, Nature (London) 118, 516 (1926).
16. P. S. Wesson and J. Ponce de Leon, Astron. Astrophys. 294, 1 (1995).
17. J. Ponce de Leon, Gen. Relativ. Gravit. 20, 539 (1988).
18. P. S. Wesson, Astrophys. J. 394, 19 (1992).
19. P. S. Wesson and H. Liu, Astrophys. J. 440, 1 (1995).
20. That the extra coordinate (formula presented) in induced matter theory is related to rest mass is indicated by several arguments. (a) All of mechanics depends on base units of length, time, and mass. So if the former two can be treated as coordinates then maybe the last should also. Dimensionally, (formula presented) = Gm/csup 2 allows us to treat the rest mass m of a particle as a length coordinate, in analogy with (formula presented) = ct. (b) Metrics, such as those for solitons protect Ref. 5 Ref. 6 Ref. 7 Ref. 8, that do not depend on (formula presented) yield only the equation of state for photons, while metrics, such as those for cosmologies protect Ref. 17 Ref. 18 Ref. 19, that do depend on (formula presented) are necessary to obtain equations of state for fluids composed of massive particles. (c) The metrics (formula presented) = (formula presented)-d (formula presented) -d (formula presented) and (formula presented) -d (formula presented) -(formula presented) d (formula presented) are related by the coordinate transformation T= (formula presented) /4+ ln [(formula presented) /4- ln [(formula presented)]. The former metric is flat, while the latter for a particle at rest in 3 space (dσ/ds =0) and viewed on a hypersurface (ψ= const) gives an action principle δ intψdt =0 that is formally the same as that of particle physics if ψr =m in the local, low velocity limit. The same is true of cosmological metrics protect Ref. 17 Ref. 18 Ref. 19. This agrees with the view from quantum field theory that the rest masses of elementary particles are generated spontaneously in a conformally invariant theory that includes a scalar dilaton field or Nambu Goldstone boson in Minkowski space. A corollary of the belief that (formula presented) is not merely a length (or time) is that the extra part of the metric can have either sign without running afoul of closed timelike paths and causality problems. These topics are discussed at greater length in the literature on 5D induced matter theory.
21. D. Kramer, H. Stephani, M. A. H. MacCallum, and E. Herlt, Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge, England, 1980).
22. R. N. Henriksen and P. S. Wesson, Astrophys. Space Sci. 53, 429 (1978).
23. R. N. Henriksen and P. S. Wesson, Astrophys. Space Sci. 53, 445 (1978).
24. P. S. Wesson and H. Liu, Phys. Lett. B 298, 69 (1993).
25. W. B. Bonnor, Gen. Relativ. Gravit. 21, 1143 (1989).
26. W. B. Bonnor and F. I. Cooperstock, Phys. Lett. A 139, 442 (1989).
27. N. A. Bahcall and L. M. Lubin, Astrophys. J. 426, 513 (1994).
28. M. M. Crone, A. E. Evrard and D. O. Richstone, Astrophys. J. 434, 402 (1994).
29. C. S. Kochanek, Astrophys. J. 436, 56 (1994).
30. M. Girardi, A. Biviano, G. Giuricin, F. Mardirossian and M. Mezzetti, Astrophys. J. 438, 527 (1995).
31. J. M. Overduin, P. Lim, andP. S. Wesson, in Proceedings of the 7th Marcel Grossmann Meeting on General Relativity, edited by M. Kaiser (World Scientific, Singapore, in press).