Study of Einstein Solutions And Symmetries of Type N Pure Radiation Field
In the present research paper, we study Einstein solitons with a physical interpretation of the notion of the vector field associated with Einstein solitons. We investigate the geometrical symmetries of Petrov type N pure radiation fields along the vector field also associated with Einstein solitons.
2. Ahsan, Z., A Symmetry property of the spacetime of general relativity in terms of the space matter tensor, Brazilin Journal of Phys., 26(3) (1996), 572-576.
3. Ahsan, Z., Interacting radiation field, Indian J. Pure App. Maths., 31(2) (2000), 215-225.
4. Ahsan, Z., On a geometrical symmetry of the spacetime of general relativity, Bull. Cal. Math. Soc., 97 (3) (2005) 191-200.
5. Ali, M and Ahsan, Z., Ricci Solitons and Symmetries of spacetime manifold of General relativity, Glob. J. Adv. Res. Class. Mod. Geom., 1 (2) (2013) 75-84.
6. Ali, M., and Ahsan, Z., Gravitational field of Schwarzschild soliton. Arab J. Math. SCi. http://dx.doi.org/10.1016/j/ajmsc.2013.10.003.
7. Akbar, M. M., and Woolger, E., Ricci soliton and Einstein scalar field theory., Class. Quantum Grav. 26(2009), 55015.
8. B List. Evolution of an extended Ricci flow system, Phd thesis 2005.
9. Catino, G. and Mazzieri, Gradient Einstein solitons, Nonlinear Anal. 132 (2016), 66-74.
10. Davis, W. R., Green, L. H. and Norris, L. K., Relativistic matter fields admitting Ricci collineation and elated conservation laws, II Nuovo Cimento, 34 B (1976), 256-280.
11. Duggal, K. L., Relativistic fluids with shear and timelike conformal collineation J. Math. Phys., 28(1987) 2700-2705.
12. Katzin, G. H. and Levine, J., Application of Lie derivatives to the symmetries, Geodesic mappings and first integrals in Riemannian spaces, J. Colloq. Math., 26 (1972) 21-38.
13. Norris, L. K., Green L. H., and Davis, W. R., Fluid space time including electromagnetic fields admitting symmetry mappings belonging to the family of contracted Ricci collineations, J. Math. Phys., 18(1977) 1305-1312.
14. Stepanov, S. E. and Shelepova, V. N., A note on Ricci solitons, Mathmaticheskie Zametici 86, (3) (2009), 474-477.
15. Stephani, H., Krammer, D., McCallum, M. and Herlt, E., Exact solutions of Einstein field equations, Cambridge Univ. Press, Cambridge (2003).
16. Yano, K., The theory of Lie derivative and its Application, Vol III, North Holand publishing co. Amsterdom p. Noordhoff L.T.D. Groningen (1957).
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