Geodesic
Canonical formulation of the embedded theory of gravity equivalent to
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 2, pp. 271-288 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the approach in which independent variables describing gravity are functions of the space–time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form that requires imposing additional constraints, which are a part of Einstein's equations. As a result, we obtain a theory with an eight-parameter gauge symmetry. This theory becomes equivalent to Einstein's general relativity either after partial gauge fixing or after rewriting the metric in the form that is invariant under the additional gauge transformations. We write the action for such a theory.
Keywords: isometric embedding, theory of gravity, canonical formalism. 
@article{TMF_2007_153_2_a5,
     author = {S. A. Paston and V. A. Franke},
     title = {Canonical formulation of the embedded theory of gravity equivalent to},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {271--288},
     year = {2007},
     volume = {153},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_2_a5/}
}
TY  - JOUR
AU  - S. A. Paston
AU  - V. A. Franke
TI  - Canonical formulation of the embedded theory of gravity equivalent to
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 271
EP  - 288
VL  - 153
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_153_2_a5/
LA  - ru
ID  - TMF_2007_153_2_a5
ER  - 
%0 Journal Article
%A S. A. Paston
%A V. A. Franke
%T Canonical formulation of the embedded theory of gravity equivalent to
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 271-288
%V 153
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2007_153_2_a5/
%G ru
%F TMF_2007_153_2_a5
S. A. Paston; V. A. Franke. Canonical formulation of the embedded theory of gravity equivalent to. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 2, pp. 271-288. http://geodesic.mathdoc.fr/item/TMF_2007_153_2_a5/

[1] M. Janet, Ann. Soc. Pol. Math., 5 (1926), 38 | Zbl

[2] E. Cartan, Ann. Soc. Pol. Math., 6 (1927), 1 | Zbl

[3] Sh. Kobayasi, K. Nomidzu, Osnovy differentsialnoi geometrii, t. 1, 2, Nauka, M., 1981 | MR | MR | Zbl

[4] A. Friedman, J. Math. Mech., 10 (1961), 625 | MR | Zbl

[5] T. Regge, C. Teitelboim, “General relativity a la string: a progress report”, Proceedings of the First Marcel Grossmann Meeting on General Relativity (Trieste, Italy, 1975), ed. R. Ruffini, North-Holland, Amsterdam, 1977, 77

[6] S. A. Paston, V. A. Franke, “The gravity as a theory of embedding of space-time into the flat space of higher demensions”, Proceedings of the XV Int. V. A. Fock School for Advances of Physics 2005, ed. V. Yu. Novozhilov, Publ. St. Petersburg State Univ., St. Petersburg, 2006, 34

[7] S. Deser, F. A. E. Pirani, D. C. Robinson, Phys. Rev. D, 14 (1976), 3301 | DOI | MR

[8] V. Tapia, Class. Quantum Grav., 6 (1989), L49 | DOI | MR | Zbl

[9] R. Arnowitt, S. Deser, C. W. Misner, “The dynamics of general relativity”, Gravitation: an Introduction to Current Research, ch. 7, ed. L. Witten, Wiley, New York, 1962, 227 ; gr-qc/0405109 | MR | Zbl

[10] V. A. Franke, V. Tapia, Nuovo Cimento B (11), 107:6 (1992), 611 | DOI | MR

[11] M. Pavsic, V. Tapia, Resource letter on geometrical results for embeddings and branes, gr-qc/0010045