zbMATH — the first resource for mathematics

Multiplane gravitational lensing. I: Morse theory and image counting. (English) Zbl 0854.57027
Summary: The image counting problem for gravitational lensing by general matter deflectors distributed over finitely many lens planes is considered. Counting formulas and lower bounds are found via Morse theory for the number of images of a point source not on a caustic. Images are counted within a compact region \(D\) not necessarily assumed to properly contain the deflector space. In addition it is shown that Morse theory is applicable because multiplane time-delay maps \(T_y\) generically satisfy the Morse boundary conditions relative to \(D\). All results obtained depend only on the topological properties induced in the lens planes by the deflector potentials and the behavior of \(\text{grad } T_y\) at boundary points of \(D\).

57R99 Differential topology
83C99 General relativity
Full Text: DOI
[1] DOI: 10.1126/science.84.2188.506 · Zbl 0015.27806 · doi:10.1126/science.84.2188.506
[2] Schneider P., Astron. Astrophys. 164 pp 237– (1986)
[3] DOI: 10.1093/mnras/235.4.1073 · doi:10.1093/mnras/235.4.1073
[4] DOI: 10.1063/1.529667 · doi:10.1063/1.529667
[5] DOI: 10.1063/1.530321 · Zbl 0783.58093 · doi:10.1063/1.530321
[6] Witt H., Astron. Astrophys. 236 pp 311– (1990)
[7] Erdl H., Astron. Astrophys. 268 pp 453– (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.