Geodesic
Classification of minimum global embeddings for nonrotating black holes
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 213-223 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of the existence of global embeddings of metrics of spherically symmetric black holes into an ambient space with the minimum possible dimension. We classify the possible types of embeddings by the type of realization of the metric symmetry by ambient space symmetries. For the Schwarzschild, Schwarzschild–de Sitter, and Reissner–Nordström black holes, we prove that the known global embeddings are the only ones. We obtain a new global embedding for the Reissner–Nordström–de Sitter metrics and prove that constructing such embeddings is impossible for the Schwarzschild–anti-de Sitter metric. We also discuss the possibility of constructing global embeddings of the Reissner–Nordström–anti-de Sitter metric.
Keywords: gravity theory, isometric embedding, embedding theory, black hole, additional dimension. 
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A. A. Sheikin; S. A. Paston. Classification of minimum global embeddings for nonrotating black holes. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 213-223. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a19/

[1] A. Friedman, J. Math. Mech., 10 (1961), 625–649 | MR | Zbl

[2] D. Kramer, Kh. Shtefani, M. Mak-Kallum, E. Kherlt, Tochnye resheniya uravnenii Einshteina, Energoizdat, M., 1982 | MR

[3] S. Willison, A Re-examination of the Isometric embedding approach to General Relativity, arXiv: 1311.6203

[4] E. Kasner, Am. J. Math., 43:2 (1921), 130–133 | DOI | MR | Zbl

[5] C. Fronsdal, Phys. Rev., 116:3 (1959), 778–781 | DOI | MR | Zbl

[6] T. Regge, C. Teitelboim, “General relativity à la string: a progress report”, Proceedings of the First Marcel Grossmann Meeting (Trieste, Italy, 1975), ed. R. Ruffini, North Holland, Amsterdam, 1977, 77–88

[7] S. Deser, F. A. E. Pirani, D. C. Robinson, Phys. Rev. D, 14:12 (1976), 3301–3303 | DOI

[8] M. Pavsic, Phys. Lett. A, 107 (1985), 66–70 | DOI | MR | Zbl

[9] + V. Tapia, Class. Quantum Grav., 6:3 (1989), L49–L56 | DOI | MR | Zbl

[10] M. D. Maia, Class. Quantum Grav., 6:2 (1989), 173–183 | DOI | MR | Zbl

[11] I. A. Bandos, Modern Phys. Lett. A, 12:11 (1997), 799–810, arXiv: hep-th/9608093 | DOI | MR | Zbl

[12] D. Karasik, A. Davidson, Phys. Rev. D, 67:6 (2003), 064012, 17 pp., arXiv: gr-qc/0207061 | DOI | MR | Zbl

[13] S. A. Paston, V. A. Franke, TMF, 153:2 (2007), 271–288, arXiv: 0711.0576 | DOI | MR | Zbl

[14] L. D. Faddeev, TMF, 166:3 (2011), 323–335, arXiv: ; L. D. Faddeev, New action for the Hilbert-Einstein equations, arXiv: ; 3+1 decomposition in the new action for the Einstein theory of gravitation, arXiv: 0911.02820906.46391003.2311 | DOI | MR | Zbl

[15] S. A. Paston, A. A. Sheykin, Internat. J. Modern Phys. D, 21:5 (2012), 1250043, 19 pp., arXiv: 1106.5212 | DOI | MR | Zbl

[16] S. Deser, O. Levin, Phys. Rev. D, 59:6 (1999), 064004, 7 pp., arXiv: hep-th/9809159 | DOI | MR

[17] S. A. Paston, JHEP, 06 (2014), 122, arXiv: 1402.3975 | DOI | MR

[18] S. A. Paston, Hawking into Unruh mapping for embeddings of hyperbolic type, Class. Quantum Grav., 32, no. 14, 2015, arXiv: 1411.4329 | DOI | MR | Zbl

[19] Y.-Z. Chu, J. Math. Phys., 55:9 (2014), 092501, 16 pp., arXiv: 1305.6933 | DOI | MR | Zbl

[20] K. R. Karmarkar, Proc. Indian Acad. Sci. A, 27:1 (1948), 56–60 | MR

[21] T. Fujitani, M. Ikeda, M. Matsumoto, J. Math. Kyoto Univ., 1:1 (1961), 43–61 | DOI | MR | Zbl

[22] A. Davidson, U. Paz, Found. Phys., 30:5 (2000), 785–794 | DOI | MR

[23] S. A. Paston, A. A. Sheykin, Class. Quantum Grav., 29:9 (2012), 095022, 17 pp., arXiv: 1202.1204 | DOI | MR | Zbl

[24] J. Rosen, Rev. Modern Phys., 37:1 (1965), 204–214 | DOI | MR | Zbl

[25] J. Rosen, Nuovo Cimento, 38 (1965), 631–633 | DOI | MR | Zbl

[26] S. A. Paston, A. A. Sheykin, SIGMA, 10 (2014), 003, 10 pp., arXiv: 1304.6550 | MR | Zbl

[27] Y.-W. Kim, Y.-J. Park, K.-S. Soh, Phys. Rev. D, 62:10 (2000), 104020, 6 pp., arXiv: gr-qc/0001045 | DOI | MR

[28] A. A. Sheykin, D. A. Grad, S. A. Paston, PoS(QFTHEP2013), 091, arXiv: 1401.7820

[29] R. R. Kuzeev, Gravitatsiya i teoriya otnositelnosti, 18 (1981), 75–82 | MR

[30] R. R. Kuzeev, Gravitatsiya i teoriya otnositelnosti, 21 (1984), 123–126 | MR

[31] S.-T. Hong, S.-W. Kim, J. Korean Phys. Soc., 49 (2006), S748–S754, arXiv: gr-qc/0503079

[32] L. Songxin, J. J. David, J. Symbolic Comput., 44:10 (2009), 1487–1501 | DOI | MR | Zbl