# Cylindrically and axially symmetric wormholes. Throats in vacuum?

*K.A. Bronnikov, M.V. Skvortsova*^{1}, K.A. Bronnikov^{2}, K.A. Bronnikov^{3}

(1) Center for Gravitation and Fundamental Metrology, VNIIMS, Ozernaya ul. 46, Moscow, 119361, Russia

(2) Institute of Gravitation and Cosmology, PFUR, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

(3) I. Kant Baltic Federal University, ul. Al. Nevskogo 14, Kaliningrad, 236041, Russia

### Abstract

This brief review discusses the existence conditions of wormhole throats and wormholes as global configurations in general relativity under the assumptions of cylindrical and axial symmetries. It is pointed out, in particular, that wormhole throats can exist in static, cylindrically symmetric space-times under slightly different conditions as compared with spherical symmetry. In cylindrically symmetric spacetime with rotation, throats can exist in the presence of ordinary matter or even in vacuum; however, there are substantial difficulties in obtaining asymptotically flat wormhole configurations without exotic matter: such examples are yet to be found. Some features of interest are discussed in static, axially symmetric configurations, including wormholes with singular rings and wrongly seeming regular wormhole throats in the Zipoy-Voorhees vacuum space-time.

### References

- M. Morris, K. S. Thorne, and U. Yurtsever, Phys. Rev. Lett.
**61**, 1446 (1988).
- M. Visser,
*Lorentzian Wormholes: from Einstein to Hawking* (AIP, Woodbury, 1995).
- K. A. Bronnikov and S. G. Rubin,
*Black Holes, Cosmology and Extra Dimensions* (World Scientific, 2012).
- A. Doroshkevich, J. Hansen, I. Novikov, and A. Shatskiy, Int. J. Mod. Phys. D
**18**, 1665 (2009), arXiv: 0812.0702.
- T. Harko, Z. Kovacs, and F. S. N. Lobo, Phys. Rev. D
**79**, 064001 (2009); arXiv: 0901.3926.
- A. A. Kirillov and E. P. Savelova, Grav. Cosmol.
**19**, 92 (2013).
- E. P. Savelova, Grav. Cosmol.
**19**, 101 (2013).
- D. Hochberg and M. Visser, Phys. Rev. D
**56**, 4745 (1997); gr-qc/9704082.
- D. Zipoy, J. Math. Phys.
**7**, 1137 (1966).
- K. A. Bronnikov and J. C. Fabris, Class. Quantum Grav.
**14**, 831 (1997).
- B. H. Voorhees, Phys. Rev. D
**2**, 2119 (1970).
- S. V. Krasnikov, Grav. Cosmol.
**19**, 54 (2013).
- K. A. Bronnikov and J. P. S. Lemos, Phys. Rev. D
**79**, 104019 (2009); arXiv: 0902.2360.
- V. G. Krechet, Izv. Vuzov, Fiz., No. 10, 57 (2007).
- V. G. Krechet and D. V. Sadovnikov, Grav. Cosmol.
**13**, 269 (2007).
- V. G. Krechet and D. V. Sadovnikov, Grav. Cosmol.
**15**, 337 (2009); arXiv: 0912.2181.
- K. A. Bronnikov, V. G. Krechet, and J. P. S. Lemos, Phys. Rev. D
**87**, 084060 (2013); arXiv: 1303.2993.
- K. A. Bronnikov, Acta Phys. Pol. B
**4**, 251 (1973).
- H. Ellis, J. Math. Phys.
**14**, 104 (1973).
- K. A. Bronnikov, L. N. Lipatova, I. D. Novikov, and A. A. Shatskiy, Grav. Cosmol.
**19**, 269 (2013).
- P. K. F. Kuhfittig, Phys. Rev.D
**67**, 064015 (2003); gr-qc/0401028.
- T. Matos,
*Class of Einstein-Maxwell phantom fields: rotating and magnetised wormholes*, arXiv: 0902.4439.
- A. I. Egorov, P. E. Kashargin, and S. V. Sushkov,
*Scalar multi-wormholes*. Space, Time and Fundamental Interactions, No. 1, 5 (2012).

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