Multidimensional GravityNo Access

EMBEDDING VERSUS IMMERSION IN GENERAL RELATIVITY

EDMUNDO M. MONTE

Departamento de Fisica, Universidade Federal da Paraiba, 58059-970, Joao Pessoa, Paraiba, Brazil

https://doi.org/10.1142/S0217751X09044887Cited by:1 (Source: Crossref)

Abstract

We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory, since the causal structure of the immersed space-time is not preserved by the immersion.

Keywords:

PACS: 02.40.Ky, 04.20.Cv, 04.50.Kd

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

E. Kasner, Am. J. Math. 43, 130 (1921), DOI: 10.2307/2370246. Crossref, Web of Science, Google Scholar
T. Kaluza, Sitzunger. Preuss. Akad. Wiss. Berlin, Phys. Math. K1, 33 (1921). O. Klein, Z. Phys. 37, 895 (1926) . Google Scholar
N. Arkani-Hamedet al., Phys. Lett. B 429, 263 (1998). Crossref, Web of Science, ADS, Google Scholar
L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999), DOI: 10.1103/PhysRevLett.83.3370. Crossref, Web of Science, ADS, Google Scholar
K. Maedaet al., Phys. Rev. D 62, 24012 (2000), DOI: 10.1103/PhysRevD.62.124009. Crossref, Web of Science, Google Scholar
M. D. Maia and E. M. Monte, Phys. Lett. A 297, 9 (2002), DOI: 10.1016/S0375-9601(02)00182-2. Crossref, Web of Science, ADS, Google Scholar
R. Kerner, Ann. Inst. H. Poincaré 9, 141 (1968). Google Scholar
H. Goenner , General Relativity and Gravitation I , ed. A. Held ( Plenum Press , New York , 1980 ) . Google Scholar
M. P. Carmo , Riemannian Geometry ( Birkhäuser , Boston , 1993 ) . Google Scholar
M. D. Maia and E. M. Monte, Mat. Contemp. 13, 229 (1997). Google Scholar
S. Hawking and G. Ellis , The Large Scale Structure of Space-Time ( Cambridge University Press , Cambridge , 1973 ) . Crossref, Google Scholar
B. O'Neill , Semi-Riemannian Geometry ( Academic Press , New York , 1970 ) . Google Scholar
C. Fronsdal, Phys. Rev. 116, 778 (1959), DOI: 10.1103/PhysRev.116.778. Crossref, Web of Science, ADS, Google Scholar