Abstract
In this paper, we study the gravitational perturbation of traversable wormhole spacetime, especially the Morris-Thorne wormhole spacetime, by using the linearized theory of gravity. We restrict our interest to the first order term and ignore the higher order terms. We assume that the perturbation is axisymmetric. We also assume that the time dependence follows the Fourier decomposition and the angular dependence is expressed in terms of the Legendre functions. As a result, we derive the gravitational perturbation equation of traversable wormhole in terms of a single linear second-order differential equation. As a consequence, we could analyze the unstability of the spacetime with the effective potentials. Furthermore, we consider the interaction between the external gravitational perturbation and the exotic matter, constituting traversable wormholes and its effect on the stability of traversable wormholes.
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References
P. A. R. Ade et al. (Planck Collaboration), Astronomy and Astrophysics 571, 1 (2014).
A. Melchiorri, L. Mersini, C. J. Odman and M. Trodden, Phys. Rev. D 68, 043509 (2003).
E. J. Copeland, M. Sami and S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006).
M. S. Morris and K. S. Thorne, Am. J Phys. 56, 395 (1988).
VIRGO, LIGP SCIENTIFIC collaborations, B. P. Abbott et al. Phys. Rev. Lett. 116, 061102 (2016).
VIRGO, LIGP SCIENTIFIC collaborations, B. P. Abbott et al. Phys. Rev. Lett. 116, 221101 (2016).
R. A. Konoplya and A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011).
K. D. Kokkotas and B. G. Schmidt, Living Rev. Rel. 2, 2 (1999).
R. A. Konoplya and C. Molina, Phys. Rev. D 71, 124009 (2005).
J. P. S. Lemos, F. S. N. Lobo and S. Oliverira, Phys. Rev. D 68, 064004 (2003).
V. Cardoso and J. P. S. Lemos, Phys. Rev. D 63, 124015 (2001).
S. A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).
E. Berti and K. D. Kokkotas, Phys. Rev. D 67, 064020 (2003).
S.-W. Kim, Nuovo Clim. 120B, 1235 (2005).
P. E. Kashargin and S. V. Sushkov, Phys. Rev. D 78, 064071 (2008).
K. A. Bronnikov, R. A. Konoplya and A. Zhidenko, Phys. Rev. D. D 86, 024028 (2012).
A. A. Abdujabbarov and B. J. Ahmedov, Astrophys. Space Sci. 321, 225 (2009).
R. A. Konoplya and A. Zhidenko, J. Cos. Astropart. Phys. 12, 043 (2016).
Y. Kang and S.-W. Kim, J. Korean Phys. Soc. 65, 913 (2014).
S. Chandrasekhar, Proc. Roy. Soc. Lond. A 343, 289 (1975).
J. L. Friedman, Proc. Roy. Soc. Lond. A 335, 163 (1973).
S. Sushkov, Phys. Rev. D 71, 043520 (2005).
M. Sullivan et al., Astrophys. J. 737, 102 (2011).
F. S. N. Lobo, Phys. Rev. D 71, 084011 (2005).
E. Komatsu, Astrophys. J. Suppl. 192, 18 (2011).
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Kang, Y., Kim, SW. Gravitational Perturbation of Traversable Wormhole Spacetime and the Stability. J. Korean Phys. Soc. 73, 1800–1807 (2018). https://doi.org/10.3938/jkps.73.1800
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DOI: https://doi.org/10.3938/jkps.73.1800