Integrability analysis of a conformal equation in relativity |
| |
Authors: | K. S. Govinder P. G. L. Leach S. D. Maharaj |
| |
Affiliation: | (1) Department of Mathematics and Applied Mathematics, University of Natal, 4014 Dalbridge, South Africa;(2) University of Natal, Johannesburg, South Africa;(3) University of Witwatersrand, Johannesburg, South Africa |
| |
Abstract: | In 1987 C. C. Dyer, G. C. McVittie, and L. M. Oattes derived the (two) field equations for shear-free, spherically symmetric perfect fluid spacetimes which admit a conformai symmetry. We use the techniques of the Lie and Painlevé analyses of differential equations to find solutions of these equations. The concept of a pseudo-partial Painlevé property is introduced for the first time which could assist in finding solutions to equations that do not possess the Painlevé property. The pseudo-partial Painlevé property throws light on the distinction between the classes of solutions found independently by P. Havas and M. Wyman. We find a solution for all values of a particular parameter for the first field equation and link it to the solution of the second equation. We indicate why we believe that the first field equation cannot be solved in general. Both techniques produce similar results and demonstrate the close relationship between the Lie and Painlevé analyses. We also show that both of the field equations of Dyeret al. may be reduced to the same Emden-Fowler equation of index two. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|