Abstract
Conformal Killing vectors (CKVs) in static plane symmetric space–times were recently studied by Saifullah and Yazdan, who concluded by remarking that static plane symmetric space–times do not admit any proper CKV except in the case where these space–times are conformally flat. We present some non-conformally flat static plane symmetric space–time metrics admitting proper CKVs. For these space–times, we also investigate a special type of CKVs, known as inheriting CKVs.
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References
H. Stephani, D. Kramer, M. Maccallum, C. Hoenselears, and E. Herlt, Exact Solutions of Einstein’s Field Equations, Cambridge Univ. Press, Cambridge (2003).
G. S. Hall, Symmetries and Curvature Structure in General Relativity (World Sci. Lect. Notes Phys., Vol. 46), World Scientific, Singapore (2004).
M. Tsamparlis, A. Paliathanasis, and L. Karpathopoulos, “Exact solutions of Bianchi I spacetimes which admit conformal Killing vectors,” Gen. Relativ. Gravit., 47, 15 (2015).
R. Maartens, D. P. Mason, and M. Tsamparlis, “Kinematic and dynamic properties of conformal Killing vectors in anisotropic fluids,” J. Math. Phys., 27, 2987–2994 (1986).
R. Marteens, S. D. Maharaj, and B. O. J. Tupper, “Conformal motions in static spherical spacetimes,” Class. Q. Grav., 13, 317–318 (1996).
A. A. Coley and B. O. J. Tupper, “Affine conformal vectors in space-time,” J. Math. Phys., 33, 1754–1764 (1992).
A. A. Coley and B. O. J. Tupper, “Spacetimes admitting inheriting conformal Killing vector fields,” Class. Q. Grav., 7, 1961–1981 (1990).
R. Maartens and S. D. Maharaj, “Conformal Killing vectors in Robertson–Walker spacetimes,” Class. Q. Grav., 3, 1005–1011 (1986).
G. S. Hall and J. D. Steele, “Conformal vector fields in general relativity,” J. Math. Phys., 32, 1847–1853 (1991).
S. Moopanar and S. D. Maharaj, “Relativistic shear-free fluids with symmetry,” J. Eng. Math., 82, 125–131 (2013).
R. Marteens, S. D. Maharaj, and B. O. J. Tupper, “General solution and classification of conformal motions in static spherical spacetimes,” Class. Q. Grav., 12, 2577–2586 (1995).
G. S. Hall and M. S. Capocci, “Classification and conformal symmetry in three-dimensional space–times,” J. Math. Phys., 40, 1466–1478 (1999).
D. Kramer and J. Carot, “Conformal symmetry of perfect fluids in general relativity,” J. Math. Phys., 32, 1857–1860 (1991).
G. S. Hall and J. Carot, “Conformal symmetries in null Einstein–Maxwell fields,” Class. Q. Grav., 11, 475–480 (1994).
R. Marteens and S. D. Maharaj, “Conformal symmetries of pp-waves,” Class. Q. Grav., 8, 503–514 (1991).
J. Castejón-Amenedo and A. A. Coley, “Exact solutions with conformal Killing vector fields,” Class. Q. Grav., 9, 2203–2215 (1992).
K. Saifullah and Shair-E-Yazdan, “Conformal motions in plane symmetric static space–times,” Internat. J. Modern Phys. D, 18, 71–81 (2009).
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 1, pp. 172–182, April, 2017.
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Hussain, T., Khan, S., Bokhari, A.H. et al. Proper conformal Killing vectors in static plane symmetric space–times. Theor Math Phys 191, 620–629 (2017). https://doi.org/10.1134/S0040577917040110
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DOI: https://doi.org/10.1134/S0040577917040110