Iterative Approach to Gravitational Lensing Theory

Details Iterative Approach to Gravitational Lensing Theory Iterative Approach to Gravitational Lensing Theory

1999-08-31

arxiv.org/abs/gr-qc/9908082v2

Phys.Rev. D61 (2000) 104007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 2 figures, submitted to Phys.Rev.D, minor revisions, new references

Scientific paper

10.1103/PhysRevD.61.104007

We develop an iterative approach to gravitational lensing theory based on approximate solutions of the null geodesic equations. The approach can be employed in any space-time which is ``close'' to a space-time in which the null geodesic equations can be completely integrated, such as Minkowski space-time, Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate the method, we construct the iterative gravitational lens equations and time of arrival equation for a single Schwarzschild lens. This example motivates a discussion of the relationship between the iterative approach, the standard thin lens formulation, and an exact formulation of gravitational lensing.

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