Deviation of geodesics in FLRW spacetime geometries

Details Deviation of geodesics in FLRW spacetime geometries Deviation of geodesics in FLRW spacetime geometries

1997-09-24

arxiv.org/abs/gr-qc/9709060v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, LaTeX 2.09, 3 *.eps figures, Contribution to the forthcoming Engelbert Sch\"{u}cking Festschrift (Springer Verlag)

Scientific paper

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--Lema\^{\i}tre--Robertson--Walker (`FLRW') models, where we assume the sources to be given by a non-interacting mixture of incoherent matter and radiation, and we also take a non-zero 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.

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