Stability of geodesic incompleteness for Robertson-Walker space-times.

Details Stability of geodesic incompleteness for Robertson-Walker space-times. Stability of geodesic incompleteness for Robertson-Walker space-times.

Mar 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981gregr..13..239b&link_type=abstract

General Relativity and Gravitation, Volume 13, Issue 3, pp.239-255

Mathematics

Logic

6

Cosmological Models

Scientific paper

Let (M, g) be a Lorentzian warped product space-timeM=(a, b)×H, g = -dt 2 ⊕fh, where -∞⩽a-∞ and (H, h) is homogeneous, then the past incompleteness of every timelike geodesic of (M,g) is stable under smallC 0 perturbations in the space Lor(M) of Lorentzian metrics forM. Also we show that if (H,h) is isotropic and (M,g) contains a past-inextendible, past-incomplete null geodesic, then the past incompleteness of all null geodesics is stable under smallC 1 perturbations in Lor(M). Given either the isotropy or homogeneity of the Riemannian factor, the background space-time (M,g) is globally hyperbolic. The results of this paper, in particular, answer a question raised by D. Lerner for big bang Robertson-Walker cosmological models affirmatively.

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