Global properties of gravitational lens maps in a Lorentzian manifold setting

Content Provider	Semantic Scholar
Author	Perlick, Volker
Copyright Year	2000
Abstract	In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere of the observer (or on part of it) and it takes values in a two-dimensional manifold representing a two-parameter family of worldlines. In this article we use methods from differential topology to characterize global properties of the lens map. Among other things, we use the mapping degree (also known as Brouwer degree) of the lens map as a tool for characterizing the number of images in gravitational lensing situations. Finally, we illustrate the general results with gravitational lensing (a) by a static string, (b) by a spherically symmetric body, (c) in asymptotically simple and empty spacetimes, and (d) in weakly perturbed Robertson-Walker spacetimes.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://qa-pubman.mpdl.mpg.de/pubman/item/escidoc:152275:1/component/escidoc:152274/3314.pdf
Alternate Webpage(s)	http://arxiv.org/pdf/gr-qc/0009105v1.pdf
Language	English
Access Restriction	Open
Subject Keyword	Amiga Walker Anatomy, Regional Approximation Brouwer fixed-point theorem Celestial coordinate system Emoticon Manifold regularization Map Population Parameter Semantics (computer science) Walkers
Content Type	Text
Resource Type	Article