Abstract
We investigate the role of a specifically warped extra dimension in constructing examples of higher dimensional spacetimes representing Lorentzian wormholes. The warping chosen is largely inspired by the well-known non-static Witten bubble of nothing, though our spacetimes are static and geometrically different. Vacuum solutions in \(D\ge 5\) dimensions and others (non-asymptotically flat) with ‘perfectly normal’ matter stress energy are interpreted as possible Lorentzian wormholes. Asymptotically flat wormholes in \(D\ge 5\) with ‘exotic matter’ and within this class of spacetimes also appear to exist in all dimensions. A wormhole-black hole correspondence via double Wick rotation is revisited and discussed. Finally, geodesic motion as well as the behaviour of geodesic congruences, in the sub-class of five dimensional, warped, vacuum wormhole spacetimes is also briefly analysed, with the aim of obtaining characteristic properties and specific signatures which may help improve our understanding of these geometries.
References
Flamm, L.: Die Grundlagen der Allgemeinen Relativitätstheorie. Ann. d. Phys. 49, 769 (1916)
Einstein, A., Rosen, N.: Phys. Rev. 48, 73 (1935)
Misner, C.W., Wheeler, J.A.: Ann. Phys. 2, 525 (1957)
Bronnikov, K.A.: Acta Phy. Pol. B4, 251 (1973)
Ellis, H.: J. Math. Phys. 14, 104 (1973)
Giddings, S., Strominger, A.: Nucl. Phys. B 306, 890 (1988)
Morris, M.S., Thorne, K.S.: Am. J. Phys. 56, 395 (1988)
Morris, M.S., Thorne, K.S., Yurtsever, U.: Phys. Rev. Letts. 61, 1446 (1988)
Kundu, A.: Wormholes and holography, an introduction, arXiv:2110.14958
Wald, R.M.: General Relativity. The University of Chicago Press, USA (1984)
Hayward, S.A., Kim, S.W., Lee, H.: Phys. Rev. D 65, 064003 (2002)
Visser, M.: Lorentzian Wormholes: from Einstein to Hawking. AIP Press, Woodbury, NY (1995)
Bronnikov, K.A., Krechet, V.G.: Phys. Rev. D 99, 084051 (2019)
Blazquez-Salcedo, J., Knoll, C., Radu, E.: Phys. Rev. Lett. 126, 101102 (2021)
Konoplya, R., Zhidenko, A.: Phys. Rev. Lett. 128, 091104 (2022)
Epstein, H., Glaser, E., Yaffe, A.: Nuovo Cimento 36, 1016 (1965)
Visser, M., Kar, S., Dadhich, N.: Phys. Rev. Letts. 90, 201102 (2003)
Kar, S., Dadhich, N., Visser, M.: Pramana 63, 859 (2004)
Harko, T., Lobo, F.S.N., Mak, M.K., Sushkov, S.V.: Phys. Rev. 87, 067504 (2013)
Bronnikov, K.A., Galiakhmetov, A.M.: Grav. Cosmo. 21, 283 (2015)
Hohmann, M.: Phys. Rev. D 89, 087503 (2014)
Shaikh, R.: Phys. Rev. D 92, 024015 (2015)
Myrzakulov, R., Sebastiani, L., Vagnozzi, S., Zerbini, S.: Class. Quant. Grav. 33, 125005 (2016)
Shaikh, R.: Phys. Rev. D 98, 064033 (2018)
Antoniou, G., Bakopoulos, A., Kanti, P., Kleihaus, B., Kunz, J.: Phys. Rev. D 101, 024033 (2020)
Zanganeh, M.K., Lobo, F.S.N., Dehghani, M.H.: Phys. Rev. D 92, 12409 (2015)
Kar, S., Lahiri, S., SenGupta, S.: Phys. Letts. B 750, 319 (2015)
Bronnikov, K.A., Skvortsova, M.V.: Grav. Cosmo. 22, 316 (2016)
Kuhfittig, P.K.F.: Phys. Rev. D 98, 064041 (2018)
Gonzalez-Diaz, P.: Phys. Rev. D 54, 6122 (1996)
Randall, L., Sundrum, R.: Phys. Rev. Letts. 83, 4690 (1999)
Witten, E.: Nucl. Phys. B 195, 481 (1982)
Kar, S.: Phys. Rev. D 105, 024213 (2022)
Sengupta, S.: Phys. Rev. D 101, 104040 (2020)
Vollick, D.: Eur. Phys. Jr. Plus 130, 157 (2015)
Roberts, M.D.: arXiv:0901.2307 (gr-qc), unpublished
Stotyn, S., Mann, R.B.: Phys. Letts. B 705, 269 (2011)
Miyamoto, U., Kudoh, H.: JHEP 12, 048 (2006)
Bah, I., Heidmann, P.: Phys. Rev. Letts. 126, 151101 (2021)
Bah, I., Heidmann, P.: JHEP 09, 147 (2021)
Collingbourne, S.: J. Math. Phys. 62, 032502 (2021). and references therein
Kar, S.: work in progress
Gregory, R., Laflamme, R.: Phys. Rev. Lett. 70, 2837 (1993)
Gregory, R., Laflamme, R.: Nucl. Phys. B 428, 399 (1994)
Gregory, R.: The Gregory-Laflamme instability, chapter in Black holes in higher, dimensions Cambridge University Press, Cambridge, UK, G. Horowitz (2012). arxiv:1107.5821
Acknowledgements
I thank the editors of this special volume for inviting me to contribute an article in this issue dedicated to the memory of Professor Thanu Padmanabhan. Thanks also to Sumanta Chakraborty, Sandipan Sengupta and Amitabh Virmani for their valuable comments and suggestions on the manuscript. It is indeed an honour for me to present this article as a modest tribute to the memory of Professor Padmanabhan.
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Kar, S. Wormholes with a warped extra dimension?. Gen Relativ Gravit 54, 66 (2022). https://doi.org/10.1007/s10714-022-02951-2
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DOI: https://doi.org/10.1007/s10714-022-02951-2