Titlebook: ;

责难

橡子

Mohammad Tehranipoor,Nisar Ahmedsion of the lens equation, i.e., to find all the images x for a given source position y. Only in the simplest cases can this be done analytically; in general, one must find all the roots of a two-dimensional system of equations. This is not trivial, in particular because the number of solutions is n

G-spot

兽群

N. O. Artyukhova,A. E. Artyukhov,J. Krmelaurnish an additional test of General Relativity; (2.) allow us to see fainter or more distant sources; and (3.) provide a means to estimate the mass of galaxies, of clusters of galaxies, and of unseen, massive aggregates of dark matter.

安定

懒惰民族

Basic facts and the observational situation,tions. This chapter is intended mainly for readers who prefer a quick look at the basic relations, e.g., between lens mass and angular separation between images, and who are not interested in the more detailed aspects of gravitational lens theory discussed in later chapters. In particular, a “guide

推迟

heterogeneous

Derivation of the lens equation,he corresponding theory must, therefore, account for (i) the bending and distortion of light bundles by nearly isolated, bound masses, and (ii) the imbedding of sources, deflectors, and observers into their cosmological environment, how this affects the propagation of light, and, in particular, the

恶心

Properties of the lens mapping, A general description of the lens mapping in the infinitesimal neighborhood of a point is given in Sect. 5.2. It leads to the concepts of magnification and critical curves and to a classification of ordinary images. In Sect. 5.3 the light-travel-time along ray bundles that correspond to GL images i

ADORE

Lensing near critical points,source plane. We assume here that it is differentiable as often as is needed. If . is the image of x. and if the Jacobian . = det . of the derivative . of . does not vanish at x(.), there exist neighborhoods of x. and y. on which . is bijective, i.e., the lens mapping is locally invertible. For an i