×

zbMATH — the first resource for mathematics

Higher dimensional wormhole geometries with compact dimensions. (English) Zbl 1010.83010
Summary: This paper studies wormhole solutions to Einstein gravity with an arbitrary number of time dependent compact dimensions and a matter-vacuum boundary. A new gauge is utilized which is particularly suited for studies of the wormhole throat. The solutions possess arbitrary functions which allow for the description of infinitely many wormhole systems of this type and, at the stellar boundary, the matter field is smoothly joined to vacuum. It turns out that the classical vacuum structure differs considerably from the four-dimensional theory and is, therefore, studied in detail. The presence of the vacuum-matter boundary and extra dimensions places interesting restrictions on the wormhole. For example, in the static case, the radial size of a weak energy condition (WEC) respecting throat is restricted by the extra dimensions. There is a critical dimension, \(D=5\), where this restriction is eliminated. In the time dependent case, one cannot respect the WEC at the throat as the time dependence actually tends the solution towards WEC violation. This differs considerably from the static case and the four-dimensional case.

MSC:
83C15 Exact solutions to problems in general relativity and gravitational theory
83E15 Kaluza-Klein and other higher-dimensional theories
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Flamm, L., Phys. Z., 17, 448, (1916)
[2] Einstein, A.; Rosen, N., Ann. phys., 2, 242, (1935)
[3] Weyl, H., Philosophy of mathematics and natural science, (1949), Princeton Univ. Press Princeton · Zbl 0033.24209
[4] Wheeler, J.A., Phys. rev., 48, 73, (1957)
[5] Misner, C.W.; Thorne, K.S.; Wheeler, J.A., Gravitation, (1973), Freeman San Francisco
[6] Dzhunushaliev, V., Wormhole with quantum throat · Zbl 0992.83047
[7] R. Garattini, On-line Proceedings of the 9th Marcel Grossman Conference, Rome, Italy, 2000
[8] Visser, M., Lorentzian wormholes from Einstein to Hawking, (1996), American Institute of Physics New York
[9] Morris, M.A.; Thorne, K.S., Am. J. phys., 56, 395, (1988)
[10] Hawking, S.W., Phys. rev. D, 46, 603, (1992)
[11] Friedmann, J.L.; Schleich, K.; Witt, D.M., Phys. rev. let., 71, 1486, (1993)
[12] Frolov, V.; Novikov, I.D., Phys. rev. D, 48, 1607, (1993)
[13] Visser, M.; Hochberg, D., ()
[14] Aros, R.O.; Zamorano, N., Phys. rev. D, 56, 6607, (1997)
[15] Torres, D.F.; Eiroa, E.F.; Romero, G.E., Mod. phys. lett. A, 16, 1849, (2001)
[16] Eiroa, E.; Torres, D.F.; Romero, G.E., Mod. phys. lett. A, 16, 973, (2001)
[17] Safonova, M.; Torres, D.F.; Romero, G.E., Mod. phys. lett. A, 16, 153, (2001)
[18] Choudhury, A.L.; Hemant, P., Hadronic J., 24, 275, (2001)
[19] Safonova, M.; Torres, D.F.; Romero, G.E., Phys. rev. D, 65, 023001, (2002)
[20] Myers, R.C.; Perry, M.J., Ann. phys., 172, 304, (1986)
[21] Bronnikov, K.A.; Melnikov, V.N., Grav. cosmol., 1, 155, (1995)
[22] Kasper, U.; Rainer, M.; Zhuk, A., Gen. relativ. gravvit., 29, 1123, (1997)
[23] V.N. Melnikov, in: Proceedings of the 8th Marcel Grossman Meeting, Jerusalem, Israel, 1997
[24] Bergliaffa, S.E.P., Mod. phys. lett. A, 15, 531, (2000)
[25] Ponce de Leon, J.; Cruz, N., Gen. relativ. gravit., 32, 1207, (2000)
[26] Kim H, H.; Moon, S.; Yee, J.H., Jhep, 0202, 046, (2002)
[27] Das, A.; DeBenedictis, A., Prog. theor. phys., 108, 119, (2002)
[28] Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G., Phys. lett. B, 429, 263, (1998)
[29] Antoniadis, I.; Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G., Phys. lett. B, 436, 257, (1998)
[30] Arkani-Hamed, N.; Dimopoulos, S.; Dvali, G., Phys. rev. D, 59, 086004, (1999)
[31] Randall, L.; Sundrum, R., Phys. rev. lett., 83, 4690, (1999)
[32] Arkani-Hamed, N.; Dimopoulos, S.; Kaloper, N.; Sundrum, R., Phys. lett. B, 480, 193, (2000)
[33] Bañados, M.; Teitelboim, C.; Zanelli, J., Phys. rev. lett., 69, 1849, (1992)
[34] DeBenedictis, A.; Das, A., Class. quantum grav., 18, 1187, (2001) · Zbl 0980.83054
[35] Morris, M.S.; Thorne, K.S.; Yurtsever, U., Phys. rev. lett., 61, 1466, (1988)
[36] Kuhfittig, P.K.F., Am. J. phys., 67, 125, (1999)
[37] Kar, S., Phys. rev. D, 49, 862, (1994)
[38] Wang, A.; Letelier, P.S., Prog. theor. phys., 94, 137, (1995)
[39] Kar, S.; Sahdev, D., Phys. rev. D, 53, 722, (1996)
[40] Anchordoqui, L.A.; Torres, D.F.; Trobo, M.L.; Bergliaffa, S.E.P., Phys. rev. D, 57, 829, (1998)
[41] Li, L., J. geom. phys., 40, 154, (2001)
[42] Hochberg, D.; Visser, M., Talk delivered to the Advanced School on Cosmology and Particle Physics, Pensicola, Spain, 1999,
[43] Hochberg, D.; Visser, M., Phys. rev. lett., 81, 746, (1998)
[44] Hayward, S., Int. J. mod. phys. D, 8, 373, (1999)
[45] Barceló, C.; Visser, M., Twilight for the energy conditions? · Zbl 1062.83509
[46] Rice, A.G., Astron. J., 116, 1009, (1998)
[47] Perlmutter, S., Astrophys. J., 517, 565, (1999)
[48] Roman, T.A., Phys. rev. D, 47, 1370, (1993)
[49] Weinberg, S., Gravitation and cosmology: principles and applications of the general theory of relativity, (1972), Wiley New York
[50] Witten, E., Nucl. phys. B, 195, 481, (1982)
[51] Shinkai, H.; Shiromizu, T., Phys. rev. D, 62, 034010, (2000)
[52] Geddes, J., Phys. rev. D, 65, 104015, (2002)
[53] Kan, N.; Shiraishi, K., Bulk fermion stars with new dimensions
[54] Birkhoff, G.D., Relativity and modern physics, (1923), Harvard Univ. Press Boston · JFM 49.0619.01
[55] Bronnikov, K.A.; Melnikov, V.N., Gen. relativ. gravit., 27, 465, (1995)
[56] Schmidt, H.J., Grav. cosmol., 3, 185, (1997)
[57] Hochberg, D.; Visser, M., Phys. rev. D, 56, 4745, (1997)
[58] Kottler, F., Ann. phys., 56, 410, (1918)
[59] Synge, J.L., Relativity: the general theory, (1964), North-Holland Amsterdam · Zbl 0148.46101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.