Geodesic
Relation between quantum effects in general relativity and embedding theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 162-178
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss results relevant to the relation between quantum effects in a Riemannian space and on the surface appearing as a result of its isometric embedding in a flat space of a higher dimension. We discuss the correspondence between the Hawking effect fixed by an observer in the Riemannian space with a horizon and the Unruh effect related to an accelerated motion of this observer in the ambient space. We present examples for which this correspondence holds and examples for which there is no correspondence. We describe the general form of the hyperbolic embedding of the metric with a horizon smoothly covering the horizon and prove that there is a correspondence between the Hawking and Unruh effects for this embedding. We also discuss the possibility of relating two-point functions in a Riemannian space and the ambient space in which it is embedded. We obtain restrictions on the geometric parameters of the embedding for which such a relation is known.
Keywords: embedding theory, correspondence between the Hawking and Unruh effects, isometric embedding, Hawking radiation, Unruh effect. 
@article{TMF_2015_185_1_a14,
     author = {S. A. Paston},
     title = {Relation between quantum effects in general relativity and embedding theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {162--178},
     year = {2015},
     volume = {185},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a14/}
}
TY  - JOUR
AU  - S. A. Paston
TI  - Relation between quantum effects in general relativity and embedding theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 162
EP  - 178
VL  - 185
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a14/
LA  - ru
ID  - TMF_2015_185_1_a14
ER  - 
%0 Journal Article
%A S. A. Paston
%T Relation between quantum effects in general relativity and embedding theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 162-178
%V 185
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a14/
%G ru
%F TMF_2015_185_1_a14
S. A. Paston. Relation between quantum effects in general relativity and embedding theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 162-178. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a14/

[1] N. Birrell, P. Devis, Kvantovannye polya v iskrivlennom prostranstve-vremeni, Mir, M., 1984 | MR

[2] A. A. Grib, S. G. Mamaev, V. M. Mostepanenko, Kvantovye effekty v intensivnykh vneshnikh polyakh, Atomizdat, M., 1980

[3] S. W. Hawking, Commun. Math. Phys., 43:3 (1975), 199–220 | DOI | MR | Zbl

[4] W. G. Unruh, Phys. Rev. D, 14:4 (1976), 870–892 | DOI

[5] A. Friedman, J. Math. Mech., 10 (1961), 625–649 | 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. Pavšič, Phys. Lett. A, 107:2 (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 (1997), 799–810, arXiv: hep-th/9608093 | DOI | MR | Zbl

[12] F. B. Estabrook, R. S. Robinson, H. R. Wahlquist, Class. Quantum Grav., 16:3 (1999), 911–918 | DOI | MR | Zbl

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

[14] M. D. Bustamante, F. Debbasch, M.-E. Brachet, Classical gravitation as free membrane dynamics, arXiv: gr-qc/0509090

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

[16] 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

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

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

[19] R. Maartens, K. Koyama, Living Reviews in Relativity, 13 (2010), lrr-2010-5, 124 pp. http://www.livingreviews.org/lrr-2010-5 | DOI

[20] S. A. Paston, TMF, 169:2 (2011), 285–296, arXiv: 1111.1104 | DOI | MR | Zbl

[21] S. Deser, O. Levin, Class. Quantum Grav., 15:12 (1998), L85–L87, arXiv: hep-th/9806223 | DOI | MR | Zbl

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

[23] M. Beciu, H. Culetu, Modern Phys. Lett. A, 14:1 (1999), 1–8 | DOI | MR

[24] 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

[25] M. Bertola, J. Bros, V. Gorini, U. Moschella, R. Schaeffer, Nucl. Phys. B, 581:1–2 (2000), 575–603, arXiv: hep-th/0003098 | DOI | MR | Zbl

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

[27] Y.-Z. Chu, A line source in Minkowski for the de Sitter spacetime scalar Green's function: Massive case, arXiv: 1310.2939 | MR

[28] P. K. Townsend, Black holes, arXiv: gr-qc/9707012

[29] W. Rindler, Am. J. Phys., 34:12 (1966), 1174–1178 | DOI

[30] J. R. Letaw, Phys. Rev. D, 22:6 (1980), 1345–1351 | DOI | MR

[31] E. T. Akhmedov, D. Singleton, Pisma v ZhETF, 86:9 (2007), 702–706, arXiv: 0705.2525

[32] J. R. Letaw, Phys. Rev. D, 23:8 (1981), 1709–1714 | DOI | MR

[33] S. Abdolrahimi, Class. Quantum Grav., 31:13 (2014), 135009, 12 pp., arXiv: 1304.4237 | DOI | Zbl

[34] L. C. Barbado, M. Visser, Phys. Rev. D, 86:8 (2012), 084011, 11 pp., arXiv: 1207.5525 | DOI | MR

[35] S. Deser, O. Levin, Class. Quantum Grav., 14:9 (1997), L163–L168, arXiv: gr-qc/9706018 | DOI | MR | Zbl

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

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

[38] N. L. Santos, O. J. C. Dias, J. P. S. Lemos, Phys. Rev. D, 70:12 (2004), 124033, 7 pp., arXiv: hep-th/0412076 | DOI | MR

[39] R.-G. Cai, Y. S. Myung, Phys. Rev. D, 83:10 (2011), 107502, 4 pp., arXiv: 1012.5709 | DOI

[40] S.-T. Hong, W. T. Kim, J. J. Oh, Y.-J. Park, Phys. Rev. D, 63:12 (2001), 127502, 4 pp., arXiv: hep-th/0103036 | DOI | MR

[41] S.-T. Hong, S.-W. Kim, Modern Phys. Lett. A, 21:10 (2006), 789–794, arXiv: gr-qc/0303059 | DOI

[42] Y.-W. Kim, J. Choi, Y.-J. Park, Phys. Rev. D, 89:4 (2014), 044004, 8 pp., arXiv: 1311.0592 | DOI

[43] H.-Z. Chen, Y. Tian, Y.-H. Gao, X.-C. Song, JHEP, 10 (2004), 011, 10 pp., arXiv: gr-qc/0409107 | DOI | MR

[44] E. J. Brynjolfsson, L. Thorlacius, JHEP, 09 (2008), 066, 13 pp., arXiv: 0805.1876 | DOI | MR

[45] R. Banerjee, B. R. Majhi, D. Roy, Corrections to Unruh effect in tunneling formalism and mapping with Hawking effect, arXiv: 0901.0466

[46] R. Banerjee, B. R. Majhi, Phys. Lett. B, 690:1 (2010), 83–86, arXiv: 1002.0985 | DOI | MR

[47] S. A. Paston, A. A. Sheykin, SIGMA, 10 (2014), 003, 10 pp., arXiv: 1304:6550 | MR | Zbl

[48] S. A. Paston, JHEP, 06 (2014), 122, 10 pp., arXiv: 1402.3975 | DOI | MR

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

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

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

[52] S. A. Paston, Gravitatsiya kak teoriya vlozheniya, LAP Lambert Academic Publ., Saarbrücken, 2012

[53] M. Bertola, D. Gouthier, Bol. Soc. Brasil. Mat. (N. S.), 32:1 (2001), 45–62 | DOI | MR | Zbl

[54] S. A. Paston, A. A. Sheikin, TMF, 175:3 (2013), 429–441, arXiv: 1306.4826 | DOI | MR | Zbl