Criteria for multiple imaging in Lorentzian manifolds

Details Criteria for multiple imaging in Lorentzian manifolds Criteria for multiple imaging in Lorentzian manifolds

Mar 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cqgra..13..529p&link_type=abstract

Classical and Quantum Gravity, Volume 13, Issue 3, pp. 529-537 (1996).

Mathematics

Logic

4

Scientific paper

In a time-oriented Lorentzian manifold (M,g), to be interpreted as a spacetime model in the sense of general relativity, there is `multiple imaging' if some point 0264-9381/13/3/016/img1 can be joined to some timelike curve 0264-9381/13/3/016/img2 in M by at least two past-pointing lightlike geodesics. (This is the Lorentzian geometry formulation of what astrophysicists call the `gravitational lens effect'.) In this paper necessary and sufficient conditions for multiple imaging are given in terms of conjugate points and in terms of cut points. It is shown that, if a past-pointing lightlike geodesic starting from p produces a conjugate point or a cut point, then there is multiple imaging for an appropriately placed source 0264-9381/13/3/016/img2. Conversely, the existence of a cut point is necessary for multiple imaging if (M,g) is strongly causal. The existence of a conjugate point, however, is necessary for multiple imaging only under much stronger restrictions on the topological and causal structure of (M,g).

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