Iterative Approach to Gravitational Lensing Theory

Abstract

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.

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

References in corpus (3)

• Spacetime perspective of Schwarzschild lensing
• Distances in Inhomogeneous Cosmological Models
• Various Approaches to Cosmological Gravitational Lensing in Inhomogeneous Models

Cited by in corpus (8)

• Schwarzschild black hole lensing
• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• Geodesic Study of Regular Hayward Black Hole
• Prospects for testing the nature of Sgr A*'s NIR flares on the basis of current VLT- and future VLTI-observations
• Dyadosphere bending of light
• Study of errors in strong gravitational lensing
• Comparative Studies of Lensing Methods
• Orbital motion of test particles in regular Hayward black hole space-time