Alberto Sánchezª, Alfredo Macíasª, and Hernando Quevedo b,c
ª Departamento de Física, Universidad Autónoma Metropolitana–Iztapalapa Apartado Postal 55–534, 09340, México, D.F., México.
b Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México Apartado Postal 70–543, México D.F. 04510, México.
c Department of Physics, University of California Davis, CA 95616.
Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005
Abstract
Numerical methods have been extensively used to investigate Gowdy models, but only recently it has been argued that solutions–generating techniques can be applied in this case to generate new solutions. In this work, we concentrate on T3 Gowdy cosmological models and shall see that a complex coordinate transformation, together with a complex change of metric functions, allows us to apply, in a straightforward manner, the well–known solution–generating techniques that have been intensively used for stationary axisymmetric solutions.
Keywords: Exact solutions; classical differential geometry; classical relativity; cosmology.
Resumen
Métodos numéricos han sido extensamente usados para investigar modelos de Gowdy, pero sólo recientemente se ha propuesto que las técnicas de generación de soluciones pueden ser aplicadas en éste caso para generar nuevas soluciones. En este trabajo nos concentraremos en los modelos cosmológicos de Gowdy T3 y mostraremos cómo una transformación coordenada compleja junto con un cambio complejo de las funciones métricas nos permite aplicar de una manera sencilla las técnicas de generación de soluciones que han sido extensamente usadas para soluciones estacionarias axisimétricas.
Descriptores: Soluciones exactas; geometría diferencial clásica; relatividad clásica; cosmología.
PACS: 04.20.Jb; 02.40.Hw; 04.20.–q; 98.80.–k
]]>DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgments
This work was supported by CONACyT grants 48601–F, and 48404–F. DGAPA–UNAM grant IN112401, and US DOE grant DE–FG03–91ER40674. A.S. wishes to acknowledge support from a CONACyT fellowship. H.Q. wishes to thank UC MEXUS for support.
References
1. R. Gowdy, Phys. Rev. Lett. 27 (1971) 826. [ Links ]
2. R. Gowdy, Ann. Phys. (N. Y.) 83 (1974) 203. [ Links ]
3. V. Moncrief, Ann. Phys. (N. Y.) 132 (1981) 87. [ Links ]
4. B. Grubisic and V. Moncrief, Phys. Rev. D. 47 (1993) 2371. [ Links ]
5. B.K. Berger and V. Moncrief, Phys. Rev. D 48 (1993) 4676. [ Links ]
6. B.K. Berger and D. Garfinkle, Phys Rev. D 57 (1998) 4767; [ Links ] D. Garflinke and M. Weaver, Phys. Rev. D 67 (2003) 124009. [ Links ]
7. V.A. Belinsky, I.M. Khalatnikov, and E.M. Lifshitz, Adv. Phys. 19 (1970) 525. [ Links ]
8. H. Quevedo and M. Ryan, in Mathematical and Quantum Aspects of Relativity and Cosmology, eds. S. Cotsakis and G.W. Gibbons (Springer Verlag, Berlin, 2000). [ Links ]
9. H. Quevedo, in Exact solutions and scalar fields in gravity: Recent results, A. Macias, J.L. Cervantes–Cota and, C. Lammerzahl (Eds.) (Kluwer Press, New York, 2001). [ Links ]
10. A.D. Rendall and M. Weaver, Class. Quantum Grav. (2001) 18 2959. [ Links ]
11. A. Sánchez, A. Macías, and H. Quevedo, J. Math. Phys. 45 (2004) 1849. [ Links ]
12. O. Obregon, H. Quevedo, and M.P Ryan, Phys. Rev. D 65 (2001) 024022. [ Links ]
13. D. Kramer, D. Stephani, E. Herlt, M. MacCallum, and E. Schmutzer, Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge, England, 1980). [ Links ]
14. E.J. Ernst,Phys. Rev. D 168 (1968) 1415. [ Links ]
15. W. Dietz, W. and C. Hoenselaers (eds.) Solutions of Einstein's Equations: Techniques and Results (Springer–Verlag, Heidelberg, 1984). [ Links ]
16. H. Quevedo, Fortschr. Phys. 38 (1990) 737. [ Links ]
17. N.R. Sibgatullin, Oscillations and Waves in Strong Gravitational and Electromagnetic Fields (Springer–Verlag, New York, 1991). [ Links ]
18. V.S. Manko, J.D. Sanabria–Gomez, and O.V . Manko, Phys. Rev. D 62 (2000) 044048. [ Links ]
19. R. Kantowski and R. Sachs, J. Math. Phys. 7 (1966) 443. [ Links ]
20. A. Krasinski, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, England, 1997). [ Links ] ]]>