Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

Abstract

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.

25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitation

References in corpus (10)

• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Universal properties of the near-horizon optical geometry
• An Atlas of Predicted Exotic Gravitational Lenses
• On the distribution of the maximum of a gaussian field with d parameters
• A Universal Magnification Theorem for Higher-Order Caustic Singularities
• The Milky Way Galaxy as a Strong Gravitational Lens
• A Lefschetz fixed point theorem in gravitational lensing
• Geometry of Universal Magnification Invariants
• A Universal Magnification Theorem II. Generic Caustics up to Codimension Five

Cited by in corpus (17)

• Gravitational lensing in the Kerr-Randers optical geometry
• Signed magnification sums for general spherical lenses
• SDSSJ2222+2745 A Gravitationally Lensed Sextuple Quasar with Maximum Image Separation of 15.1" Discovered in the Sloan Giant Arcs Survey
• Lensing by Kerr Black Holes. I: General Lens Equation and Magnification Formula
• Strong lensing, plane gravitational waves and transient flashes
• Kerr-Newman-Jacobi geometry and the deflection of charged massive particles
• Perturbing rational harmonic functions by poles
• Microlensing effects of wormholes associated to blackhole spacetimes
• Creating images by adding masses to gravitational point lenses
• Sharp parameter bounds for certain maximal point lenses
• On simple analytic models of microlensing amplification statistics
• Multiwavelength study of the gravitationally lensed blazar QSO B0218+357 between 2016 and 2020
• How constant shifts affect the zeros of certain rational harmonic functions
• Cusp Summations and Cusp Relations of Simple Quad Lenses
• Analytical Solutions of Singular Isothermal Quadrupole Lens
• The Magnification Invariant of Circularly-symmetric Lens Models
• Multiplane gravitational lenses with an abundance of images