Isaac Scientific Publishing

Theoretical Physics

On Schwarzschild anti De Sitter and Reissner-Nördstrom Wormholes

Download PDF (9635.8 KB) PP. 133 - 149 Pub. Date: December 1, 2019

DOI: 10.22606/tp.2019.44001

Author(s)

  • Oscar Brauer*
    Facultad de Ciencias, Universidad Nacional Autónoma de México
  • Miguel Socolovsky*
    Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Cd. Universitaria, 04510, Ciudad de México, México; Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föringher Ring 6, 80805, München, Germany

Abstract

We discuss the wormholes associated with the four-dimensional Schwarzschild (S4), Schwarzschild anti De Sitter (SaDS4), and Reissner-Nördstrom (RN4) black holes, in Schwarzschild, isotropic and Kruskal-Szekeres cordinates. The first two coordinate systems are valid outside the horizons, while the third one is used for the interiors. In Schwarzschild coordinates, embedding for SaDS4 exists only for a finite interval of the radial coordinate r, and similar restrictions exist for RN4. The use of the K-S coordinates allows us to give an explicit proof of the pinching-off of the bridges, making them non-traversable. The case of the extreme Reissner-Nördstrom (ERN4) is also discussed.

Keywords

Wormholes, Schwarzschild anti De Sitter, Reissner-Nordström, black holes PACS numbers: 04.70.-s, 04.70.Bw

References

[1] Kruskal, M.D. Maximal extension of Schwarzschild metric, Phys. Rev. 119, 1743-1745 (1960).

[2] Szekeres, G. On the singularities of a Riemannian manifold, Publ. Math. Debrecen 7, 285-301 (1960).

[3] Misner, C.W. and Wheeler, J.A. Classical Physics as Geometry, Ann. of Phys. 2, 525-603 (1957).

[4] Einstein, A. and Rosen, N. The particle problem in the general theory of relativity, Phys. Rev. 48, 73-77 (1935).

[5] Fuller, R.W. and Wheeler, J.A. Causality and Multiply Connected Space-Time, Phys. Rev. 128, 919-929 (1962).

[6] Carroll, S. “Spacetime and Geometry. An Introduction to General Relativity”, Addison Wesley, San Francisco (2004).

[7] Collas, P. and Klein, D. Embeddings and time evolution of the Schwarzschild wormhole, Am. J. Phys. 80, 203-210 (2012).

[8] Morris, M.S. and Thorne, K.S. Wormholes in spacetime and their use for interstellar travel: A tool for teaching General Relativity, Am. J. Phys. 56, 395-412 (1988).

[9] Visser, M. “Lorentzian Wormholes: From Einstein to Hawking”, American Institute of Physics, New York (1995).

[10] Lobo, F.S.N. “From the Flamm-Einstein-Rosen bridge to the modern renaissence of traversable wormholes”, The Fourteenth Marcel Grossmann Meeting, University of Rome “La Sapienza”, World Scientific, 409-427 (2017).

[11] Witten, E. Light Rays, Singularities, and All That, arXiv: hep-th/1901.03928v1 (2019).

[12] Flamm, L. Beiträge zur Einsteinschen Gravitationtheorie, Physikalische Zeitschrift XVII, 448-454 (1916); reprinted: Contributions to Einstein’s theory of gravitation, Gen. Relat. Gravit. 47:72 (2015).

[13] Townsend, P.K. “Black Holes”, Lecture notes, DAMTP, Cambridge (1997); arXiv: gr-qc/9707012v1.

[14] Socolovsky, M. Schwarzschild Black Hole in Anti-De Sitter Space, Adv. App. Clifford Algebras 28:18 (2018).

[15] Gao,P., Jafferis,D.L., and Wall, A.C. Traversable Wormholes via a Double Trace Deformation, arXiv: hepth/ 1608.05687v2 (2017).

[16] Maldacena, J. and Qi, X.L. Eternal traversable wormhole, arXiv: hep-th/1804.00491v3 (2018).