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Gravitational waves propagation in nondynamical Chern-Simons gravity. (English) Zbl 1431.83042

Summary: We investigate the propagation of gravitational waves in linearized Chern-Simons (CS) modified gravity by considering two nondynamical models for the coupling field \(\theta\): (i) a domain wall and (ii) a surface layer of \(\theta\), motivated by their relevance in condensed matter physics. We demonstrate that the metric and its first derivative become discontinuous for a domain wall of \(\theta\), and we determine the boundary conditions by realizing that the additional contribution to the wave equation corresponds to one of the self-adjoint extensions of the D’Alembert operator. Nevertheless, such discontinuous metric satisfies the area matching conditions introduced by Barrett. On the other hand, the propagation through a surface layer of \(\theta\) behaves similarly to the propagation of electromagnetic waves in CS extended electrodynamics. In both cases, we calculate the corresponding reflection and transmission amplitudes. As a consequence of the distributional character of the additional terms in the equations that describe wave propagation, the results obtained for the domain wall are not reproduced when the thickness of the surface layer goes to zero, as one could naively expect.

MSC:

83C35 Gravitational waves
58J28 Eta-invariants, Chern-Simons invariants
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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References:

[1] Jackiw, R. and Pi, S.-Y., Phys. Rev. D68 (2003) 104012.
[2] Smith, T. L., Erickcek, A. L., Caldwell, R. R. and Kamionkowski, M., Phys. Rev. D77 (2008) 024015.
[3] Lue, A., Wang, L. M. and Kamionkowski, M., Phys. Rev. Lett.83 (1999) 1506.
[4] Alexander, S. and Yunes, N., Phys. Rev. D75 (2007) 124022.
[5] Qi, X.-L. and Zhang, S.-C., Rev. Mod. Phys.83 (2011) 1057.
[6] Hasan, M. Z. and Kane, C. L., Rev. Mod. Phys.82 (2010) 3045.
[7] Peccei, R. D. and Quinn, H. R., Phys. Rev. Lett.38 (1977) 1440.
[8] Wilczek, F., Phys. Rev. Lett.58 (1987) 1799.
[9] Qi, X.-L., Li, R., Zang, J. and Zhang, S.-C., Science323 (2009) 1184.
[10] Karch, A., Phys. Rev. Lett.103 (2009) 171601.
[11] Obukhov, Y. N. and Hehl, F. W., Phys. Lett. A341 (2005) 357.
[12] Huerta, L. and Zanelli, J., Phys. Rev. D85 (2012) 085024.
[13] Huerta, L., Phys. Rev. D90 (2014) 105026.
[14] Martín-Ruiz, A., Cambiaso, M. and Urrutia, L. F., Phys. Rev. D92 (2015) 125015.
[15] Martín-Ruiz, A., Cambiaso, M. and Urrutia, L. F., Phys. Rev. D93 (2016) 045022.
[16] Martín-Ruiz, A., Cambiaso, M. and Urrutia, L. F., Europhys. Lett.113 (2016) 60005.
[17] Martín-Ruiz, A., Cambiaso, M. and Urrutia, L. F., Phys. Rev. D94 (2016) 085019.
[18] Wang, Z., Qi, X.-L. and Zhang, S.-C., Phys. Rev. B84 (2011) 014527.
[19] Ryu, S., Moore, J. E. and Ludwig, A. W. W., Phys. Rev. B85 (2012) 045104.
[20] Qi, X.-L., Witten, E. and Zhang, S.-C., Phys. Rev. B87 (2013) 134519.
[21] Furusaki, A., Nagaosa, N., Nomura, K., Ryu, S. and Takayanagi, T., C. R. Phys.14 (2013) 871.
[22] Nomura, K., Ryu, S., Furusaki, A. and Nagaosa, N., Phys. Rev. Lett.108 (2012) 026802.
[23] Shiozaki, K. and Fujimoto, S., Phys. Rev. B89 (2014) 054506.
[24] Sekine, A., Phys. Rev. B93 (2016) 094510.
[25] Luttinger, J. M., Phys. Rev.135 (1964) A1505.
[26] Israel, W., Phys. Rev. D15 (1977) 935.
[27] Taub, A. H., J. Math. Phys.21 (1980) 1423.
[28] Raju, C. K., J. Phys. A, Math. Gen.15 (1982) 1785.
[29] Geroch, R. and Traschen, J., Phys. Rev. D36 (1987) 1017.
[30] Clarke, C. J. S. and Dray, T., Class. Quantum. Grav.4 (1987) 265.
[31] Hogan, P. A., Phys. Rev. Lett.70 (1993) 117.
[32] Letelier, P. S. and Wang, A., J. Math. Phys.36 (1995) 3023.
[33] Podolský, J. and Veselý, K., Phys. Lett. A241 (1998) 145.
[34] Mars, M. and Senovilla, J. M. M., Class. Quantum Grav.10 (1993) 1865.
[35] Kurasov, P., J. Math. Anal. Appl.201 (1996) 297.
[36] Albeverio, S., Dabrowsi, L. and Kurasov, P., Lett. Math. Phys.45 (1998) 33.
[37] J. W. Barrett, arXiv:gr-qc/001105.
[38] Volovik, G. E., The Universe in a Helium Droplet (Clarendon, Oxford, 2003). · Zbl 1140.83412
[39] Schutz, B. F., A First Course in General Relativity, 2nd edn. (Cambridge University Press, Cambridge, 2009). · Zbl 1173.53002
[40] Padmanabhan, T., Gravitation: Foundations and Frontiers, 1st edn. (Cambridge University Press, Cambridge, 2010). · Zbl 1187.83002
[41] Griffiths, D. J., J. Phys. A, Math. Gen.26 (1993) 2265.
[42] Coutinho, F. A. B., Nogami, Y. and Perez, J. F., J. Phys. A, Math. Gen.30 (1997) 3937.
[43] Šeba, P., Rep. Math. Phys.24 (1986) 111.
[44] Christiansen, P. L., Arnbak, H. C., Zolotaryuk, A. V., Ermakov, V. N. and Gaididei, Y. B., J. Phys. A, Math. Gen.36 (2003) 7589.
[45] Toyama, F. M. and Nogami, Y., J. Phys. A, Math. Theor.40 (2007) F685.
[46] Hallnäs, M., Langmann, E. and Paufler, C., J. Phys. A: Math. Gen.38 (2005) 4957.
[47] Gadella, M., Negro, J. and Nieto, L. M., Phys. Lett. A373 (2009) 1310.
[48] Senn, P., Am. J. Phys.56 (1988) 916.
[49] Poisson, E., A Relativist’s Toolkit: The Mathemathics of Black-Hole Mechanics (Cambridge University Press, Cambridge, 2004).
[50] Brandan, M. E. and Satchler, G. E., Phys. Rep.285 (1997) 143.
[51] Alexander, S. and Yunes, N., Phys. Rev. D77 (2008) 124040.
[52] Qiang, Li. and Xu, P., Gen. Relativ. Gravit.47 (2015) 26.
[53] Abbott, B. P.et al.., Phys. Rev. Lett.116 (2016) 061102.
[54] Stone, M., Phys. Rev. B85 (2012) 184503.
[55] Sotiriou, T. P. and Faraoni, V., Rev. Mod. Phys.82 (2010) 451.
[56] De Felice, A. and Tsujikawa, S., Living Rev. Rel.13 (2010) 3.
[57] Hidaka, Y., Hirono, Y., Kimura, T. and Minami, Y., Prog. Theor. Exp. Phys.2013 (2013) 013A02.
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