Cosmological stability of Weyl conformal tensor
E. Goulart and M. Novello1
(1) Institute of Cosmology, Relativity and Astrophysics ICRA/CBPF, Rua Dr. Xavier Sigaud 150, Urca 22290-180 Rio de Janeiro, RJ-Brazil
We show that the conformal structure of the Friedmann-Robertson-Walker geometry is asymptotically stable with respect to time under arbitrary scalar perturbations. The analysis was undertaken for the Euclidean section, using the gauge-independent quasi-Maxwellian equations of motion for the perturbations. A well-known divergence theorem of non-autonomous planar dynamical systems is used to corroborate our conclusions. In other words, from a global point of view, once the geometry arrives at a FRW stage, it is not likely to leave it, even if during a certain limited interval of time it may present inhomogeneous properties.
For more information about this paper please visit Springer's Home Page of this paper.
- P. Jordan, J. Ehlers, and R. Sachs, Akad. Wiss. Lit. Mainz Abh. Math. Naturwiss. Kl. 1, 3 (1961).
- S. W. Hawking, Astrohys. J. 145, 544 (1966).
- G. F. R. Ellis, in: General Relativity and Cosmology, Proceedings of the International School of Physics "Enrico Fermi", Course XLVII (Academic, London, 1971).
- M. Novello, J. M. Salim, M. C. Motta da Silva, S. E. Joras, and R. Klippert, Phys. Rev. D 51 450 (1995) and references therein.
- E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12, 185 (1963).
- J. Bardeen, Phys. Rev. D 22 1882 (1980).
- S. W. Goode, Phys. Rev. D 39 10 (1989).
- M. Novello, J. M. Salim, M. C. Motta da Silva, S. E. Joras, and R. Klippert, Phys. Rev. D 52 730 (1995).
- M. Novello, J. M. Salim, M. C. Motta da Silva, and R. Klippert, Phys. Rev. D 54 2578 (1996).
- J. M. Stewart and M. Walker, Proc. R. Soc. London A 341, 49 (1974), and also J. M. Stewart, Class. Quant. Grav. 7 1169 (1990).
- V. I. Arnold, Mathematical Methods of Classical Mechanics, (Spriger-Verlag, 2nd ed., 1989); R. C. Hilborn, Chaos and Non-Linear Dynamics, (Oxford Univ. Press, Oxford, 2000).
- A. Erdelyi, Higher Transcendetal functions, v. I. (Caltech Bateman Manuscript Project, 1953).
- G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, 4th edition, 1995).
Back to The Contents Page