Abstract
For a perfect fluid matter, we present a study of conformal Ricci collineations (CRCs) of non-static spherically symmetric spacetimes. For non-degenerate Ricci tenor, a vector field generating CRCs is found subject to certain integrability conditions. These conditions are then solved in various cases by imposing certain restrictions on the Ricci tensor components. It is found that non-static spherically symmetric spacetimes admit 5, 6 or 15 CRCs. In the degenerate case, it is concluded that such spacetimes always admit infinite number of CRCs.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Baysal, H.; Camci, U.; Tarhan, I.; Yilmaz, I.; Yavuz, I.: Conformal collineations in string cosmology. Int. J. Mod. Phys. D 11, 463 (2002)
Bokhari, A.H.; Kashif, A.R.: Curvature collineations of some static spherically symmetric spacetimes. J. Math. Phys. 37, 3498 (1996)
Camci, U.: Matter collineations of Bianchi V spcetime. Int. J. Mod. Phys. D 14, 1023 (2005)
Camci, U.; Sahin, E.: Matter collineation classification of Bianchi type II spacetime. Gen. Relat. Gravit. 38, 1331 (2006)
Camci, U.; Sharif, M.: Matter collineations in Kantowski–Sachs, Bianchi types I and III spacetimes. Gen. Relat. Gravit. 35, 97 (2003)
Camci, U.; Yavuz, I.: Classifications of Kantowski–Sachs, Bianchi types I and III spacetimes according to Ricci collineations. Int. J. Mod. Phys. D 12, 89 (2003)
Camci, U.; Yavuz, I.; Baysal, H.; Tarhan, I.; Yilmaz, I.: Ricci collineations of the Bianchi types I and III, and Kantowski–Sachs spacetimes. Int. J. Mod. Phys. D 10, 751 (2001)
Camci, U.; Qadir, A.; Saifullah, K.: Conformal Ricci collineations of static spherically symmetric spacetimes. Commun. Theor. Phys. 49, 1527 (2008)
Duggal, K.L.: Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times. J. Math. Phys. 33, 2989 (1992)
Hall, G.S.: Symmetries and Curvature Structure in General Relativity. World Scientific, Cambridge (2004)
Herrera, L.; Jiménez, J.; Leal, L.; Ponce de Leon, J.; Esculpi, M.; Galina, V.: Anisotropic fluids and conformal motions in general relativity. J. Math. Phys. 25, 3274 (1984)
Hussain, T.; Akhtar, S.S.; Khan, S.: Ricci inheritance collineations in Bianchi type I spacetimes. Eur. Phys. J. Plus 130, 44 (2015)
Hussain, T.; Akhtar, S.S.; Bokhari, A.H.; Khan, S.: Ricci inheritance collineations in Bianchi type II spacetime. Mod. Phys. Lett. A 31, 1650102 (2016)
Hussain, T.; Musharaf, A.; Khan, S.: Ricci inheritance collineations in Kantowski–Sachs spacetimes. Int. J. Geom. Methods Mod. Phys. 13, 1650057 (2016)
Hussain, T.; Akhtar, S.S.; Khan, F.: Classification of locally rotationally symmetric Bianchi-I space-times using conformal Ricci collineations. Theor. Methods Phys. 193, 1524 (2017)
Hussain, T.; Khan, F.; Bokhari, A.H.; Akhtar, S.S.: Classification of Kantowski–Sachs metric via conformal Ricci collineations. Int. J. Geom. Methos Mod. Phys. 15, 1850006 (2018)
Khan, F.; Hussain, T.; Akhtar, S.S.: Conformal Ricci collineations in LRS Bianchi type V spacetimes with perfect fluid matter. Mod. Phys. Lett. A 32, 1750124 (2017)
Llosa, J.: Collineations of a symmetric 2-covariant tensor: Ricci collineations. J. Math. Phys. 54, 072501 (2013)
Mason, D.P.; Maartens, R.: Kinematics and dynamics of conformal collineations in relativity. J. Math. Phys. 28, 2182 (1987)
Mason, D.P.; Tsamparlis, M.: Spacelike conformal killing vectors and spacelike congruences. J. Math. Phys. 26, 2881 (1985)
Sharif, M.; Sheikh, U.: Timelike and spacelike matter inheritance vectors in specific forms of energy-momentum tensor. Int. J. Mod. Phys. A 21, 3213 (2006)
Stephani, H.; Kramer, D.; Maccallum, M.; Hoenselaers, C.; Herlt, E.: Exact Solutions of Einstein’s Field Equations, 2nd edn. Cambridge University Press, Cambridge (2003)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Khan, F., Hussain, T., Bokhari, A.H. et al. Non-static spherically symmetric spacetimes and their conformal Ricci collineations. Arab. J. Math. 9, 393–400 (2020). https://doi.org/10.1007/s40065-019-0249-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40065-019-0249-5