Abstract
Using a black hole with scalar hair, we construct a scalar thin-shell wormhole (TSW) in 2+1 dimensions by applying the Visser cut and paste technique. The surface stress, which is concentrated at the wormhole throat, is determined using the Darmois–Israel formalism. Using various gas models, we analyze the stability of the TSW. The stability region is changed by tuning the parameters l and u. We note that the obtained TSW originating from a black hole with scalar hair could be more stable with a particular value of the parameter l, but it still requires exotic matter.
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M. S. Morris and K. S. Thorne, “Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity,” Amer. J. Phys., 56, 395–412 (1988).
M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,” Phys. Rev. Lett., 61, 1446–1449 (1988).
D. Hochberg and M. Visser, “Null energy condition in dynamic wormholes,” Phys. Rev. Lett., 81, 746–749 (1998).
D. Hochberg, C. Molina-Paris, and M. Visser, “Tolman wormholes violate the strong energy condition,” Phys. Rev. Lett. D, 59, 044011 (1999).
J. L. Friedman, K. Schleich, and D. M. Witt, “Topological censorship,” Phys. Rev. Lett., 71, 1486–1489 (1993); Erratum, 75, 1872 (1995).
T. Harko, F. S. N. Lobo, M. K. Mak, and S. V. Sushkov, “Modified-gravity wormholes without exotic matter,” Phys. Rev. D, 87, 067504 (2013).
S. H. Mazharimousavi and M. Halilsoy, “3+1-dimensional thin shell wormhole with deformed throat can be supported by normal matter,” Eur. Phys. J. C, 75, 271 (2015).
M. Visser, “Traversable wormholes from surgically modified Schwarzschild spacetimes,” Nucl. Phys. B, 328, 203–212 (1989).
W. Israel, “Singular hypersurfaces and thin shells in general relativity,” Il Nuovo Cimento B, 44, 1–14 (1966).
E. Poisson and M. Visser, “Thin-shell wormholes: Linearization stability,” Phys. Rev. D, 52, 7318–7321 (1995).
S. H. Mazharimousavi and M. Halilsoy, “Counter-rotational effects on stability of (2+1)-dimensional thin-shell wormholes,” Eur. Phys. J. C, 74, 3073 (2014).
G. A. S. Dias and J. P. S. Lemos, “Thin-shell wormholes in d-dimensional general relativity: Solutions, properties, and stability,” Phys. Rev. D, 82, 084023 (2010).
M. La Camera, “On thin-shell wormholes evolving in flat FRW spacetimes,” Modern Phys. Lett. A, 26, 857–863 (2011).
A. Banerjee, “Stability of charged thin-shell wormholes in (2+1)-dimensions,” Internat. J. Theoret. Phys., 52, 2943–2958 (2013).
A. Banerjee, F. Rahaman, S. Chattopadhyay, and S. Banerjee, “Stability of non-asymptotically flat thin-shell wormholes in generalized dilaton–axion gravity,” Internat. J. Theoret. Phys., 52, 3188–3198 (2013).
A. Banerjee, F. Rahaman, K. Jotania, R. Sharma, and M. Rahaman, “Exact solutions in (2+1)-dimensional antide Sitter space–time admitting a linear or non-linear equation of state,” Astrophys. Space Sci., 355, 353–359 (2015).
P. Bhar and A. Banerjee, “Stability of thin-shell wormholes from noncommutative BTZ black hole,” Internat. J. Modern Phys. D, 24, 1550034 (2015).
N. M. Garcia, F. S. N. Lobo, and M. Visser, “Generic spherically symmetric dynamic thin-shell traversable wormholes in standard general relativity,” Phys. Rev. D, 86, 044026 (2012).
P. K. F. Kuhfittig, “On the stability of thin-shell wormholes in noncommutative geometry,” Adv. High Energy Phys., 2012, 462493 (2012).
M. Halilsoy, A. Ovgun, and S. H. Mazharimousavi, “Thin-shell wormholes from the regular Hayward black hole,” Eur. Phys. J. C, 74, 2796 (2014).
F. Darabi, “Classical Euclidean wormhole solutions in the Palatini f(\(\tilde R\) ) cosmology,” Theor. Math. Phys., 173, 1734–1742 (2012).
P. E. Kashargin and S. V. Sushkov, “Rotating thin-shell wormhole from glued Kerr spacetimes,” Gravit. Cosmol., 17, 119–125 (2011).
M. Sharif and M. Azam, “Mechanical stability of cylindrical thin-shell wormholes,” Eur. Phys. J. C, 73, 2407 (2013).
M. Sharif and M. Azam, “Stability analysis of thin-shell wormholes from charged black string,” J. Cosmol. Astropart. Phys., 04, 023 (2013).
M. Sharif and M. Azam, “Spherical thin-shell wormholes and modified Chaplygin gas,” J. Cosmol. Astropart. Phys., 05, 025 (2013).
C. Bejarano, E. F. Eiroa, and C. Simeone, “General formalism for the stability of thin-shell wormholes in 2+1 dimensions,” Eur. Phys. J. C, 74, 3015 (2014).
M. Sharif and S. Mumtaz, “Effects of charge on the stability of thin-shell wormholes,” Astrophys. Space Sci., 352, 729–736 (2014).
M. Sharif and M. Azam, “Thin-shell wormholes in Born–Infeld electrodynamics with modified Chaplygin gas,” Phys. Lett. A, 378, 2737–2742 (2014).
A. Eid, “Linearized stability of Reissner Nordstrom de-Sitter thin shell wormholes,” New Astronomy, 39, 72–75 (2015).
F. Rahaman and A. Banerjee, “Thin-shell wormholes from black holes with dilaton and monopole fields,” Internat. J. Theoret. Phys., 51, 901–911 (2012).
F. Rahaman, A. Banerjee, and I. Radinschi, “A new class of stable (2+1) dimensional thin shell wormhole,” Internat. J. Theoret. Phys., 51, 1680–1691 (2012).
F. Rahaman, P. K. F. Kuhfittig, M. Kalam, A. A. Usmani, and S. Ray, “A comparison of Horava–Lifshitz gravity and Einstein gravity through thin-shell wormhole construction,” Class. Q. Grav., 28, 155021 (2011).
F. Rahaman, K. A. Rahman, Sk. A. Rakib, and P. K. F. Kuhfittig, “Thin-shell wormholes from regular charged black holes,” Internat. J. Theoret. Phys., 49, 2364–2378 (2010).
S. H. Mazharimousavi and M. Halilsoy, “Einstein–Maxwell gravity coupled to a scalar field in 2+1 dimensions,” Eur. Phys. J. Plus, 130, 158 (2015).
S. H. Mazharimousavi, M. Halilsoy, I. Sakalli, and O. Gurtug, “Dilatonic interpolation between Reissner–Nordström and Bertotti–Robinson spacetimes with physical consequences,” Class. Q. Grav., 27, 105005 (2010).
G. Clément, J. C. Fabris, and G. T. Marques, “Hawking radiation of linear dilaton black holes,” Phys. Lett. B, 651, 54–57 (2007).
H. Pasaoglu and I. Sakalli, “Hawking radiation of linear dilaton black holes in various theories,” Internat. J. Theoret. Phys., 48, 3517–3525 (2009).
I. Sakalli, M. Halilsoy, and H. Pasaoglu, “Fading Hawking radiation,” Astrophys. Space Sci., 340, 155–160 (2012).
I. Sakalli and A. Ovgun, Europhys. Lett., 110, 10008 (2015).
I. Sakalli and A. Ovgun, “Gravitinos tunneling from traversable Lorentzian wormholes,” Astrophys. Space Sci., 359, 32 (2015).
I. Sakalli, M. Halilsoy, and H. Pasaoglu, “Entropy conservation of linear dilaton black holes in quantum corrected Hawking radiation,” Internat. J. Theoret. Phys., 50, 3212–3224 (2011).
I. Sakalli, “Dilatonic entropic force,” Internat. J. Theoret. Phys., 50, 2426–2437 (2011).
K. Lanczos, “Flächenhafte verteilung der materie in der Einsteinschen gravitationstheorie,” Ann. Phys. (Leipzig), 379, 518–540 (1924).
G. Darmois, Mémorial des Sciences Mathématiques Fascicule XXV, Gauthier-Villars, Paris (1927).
P. Musgrave and K. Lake, “Junctions and thin shells in general relativity using computer algebra: I. The Darmois–Israel formalism,” Class. Q. Gravity, 13, 1885–1899 (1996).
K. K. Nandi, Y.-Z. Zhang, and K. B. V. Kumar, “Volume integral theorem for exotic matter,” Phys. Rev. D, 70, 127503 (2004).
V. Varela, “Note on linearized stability of Schwarzschild thin-shell wormholes with variable equations of state,” Phys. Rev. D, 92, 044002 (2015).
K. A. Bronnikov, L. N. Lipatova, I. D. Novikov, and A. A. Shatskiy, “Example of a stable wormhole in general relativity,” Gravit. Cosmol., 19, 269–274 (2013).
I. D. Novikov and A. A. Shatskiy, “Stability analysis of a Morris–Thorne–Bronnikov–Ellis wormhole with pressure,” JETP, 114, 801–804 (2012).
P. K. F. Kuhfittig, “Wormholes with a barotropic equation of state admitting a one-parameter group of conformal motions,” Ann. Phys., 355, 115–120 (2015).
E. F. Eiroa and C. Simeone, “Stability of Chaplygin gas thin-shell wormholes,” Phys. Rev. D, 76, 024021 (2007).
F. S. N. Lobo, “Chaplygin traversable wormholes,” Phys. Rev. D, 73, 064028 (2006).
V. Gorini, U. Moschella, A. Y. Kamenshchik, V. Pasquier, and A. A. Starobinsky, “Tolman–Oppenheimer–Volkoff equations in the presence of the Chaplygin gas: Stars and wormholelike solutions,” Phys. Rev. D, 78, 064064 (2008).
A. Einstein and N. Rosen, “The particle problem in the general theory of relativity,” Phys. Rev., 48, 73–77 (1935).
A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev., 47, 777–780 (1935).
J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortschr. Phys., 61, 781–811 (2013).
F. S. N. Lobo, G. J. Olmo, and D. Rubiera-Garcia, “Microscopic wormholes and the geometry of entanglement,” Eur. Phys. J. C, 74, 2924 (2014).
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 1, pp. 138–149, January, 2017.
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Övgün, A., Sakalli, I. A particular thin-shell wormhole. Theor Math Phys 190, 120–129 (2017). https://doi.org/10.1134/S004057791701010X
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DOI: https://doi.org/10.1134/S004057791701010X