Deviation of Geodesics in FLRW Spacetime Geometries
The geodesic deviation equation (“GDE”) provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the Friedmann—LemaîtreRobertson—Walker (“FLRW”) models, where we assume the sources to be given by a noninteracting mixture of incoherent matter and radiation, and we also take a nonzero cosmological constant into account. For each causal case we present examples of solutions to the GDE and we discuss the interpretation of the related first integrals. The de Sitter spacetime geometry is treated separately.
KeywordsDust Microwave Anisotropy Manifold Vorticity
Unable to display preview. Download preview PDF.
- Bronstein, I. N., and K. A. Semendjajew: Taschenbuch der Mathematik, 23rd Edn. (Frankfurt/Main: Harri Deutsch, Thun, 1987).Google Scholar
- Ehlers, J.: Survey of General Relativity, in Relativity, Cosmology, and Astrophysics, Ed. W Israel (Dordrecht: Reidel, 1973).Google Scholar
- Ellis, G. F. R.: Relativistic Cosmology, in General Relativity and Cosmology,Proceedings of the XLVII Enrico Fermi Summer School, Ed. R K Sachs (New York: Academic Press, 1971).Google Scholar
- Ellis, G. F. R.: Standard Cosmology, in Vth Brazilian School on Cosmology and Gravitation,Ed. M Novello (Singapore: World Scientific, 1987).Google Scholar
- Ellis, G. F. R., and D. R. Matravers: Spatial Homogeneity and the Size of the Universe, in A Random Walk in Relativity and Cosmology (Raychaudhuri Festschrift), Eds. N Dadhich, J K Rao, J V Narlikar, and C V Vishveshswara (New Dehli: Wiley Eastern, 1985).Google Scholar
- Misner, C. W., K. S. Thorne, and J. A. Wheeler: Gravitation (San Francisco: Freeman and Co., 1973).Google Scholar
- Synge, J. L., and A. Schild: Tensor Calculus, (Toronto: University of Toronto Press, 1949). Reprinted: (New York: Dover Publ., 1978).Google Scholar
- Weinberg, S.: Gravitation and Cosmology (New York: John Wiley and Sons, 1972).Google Scholar