Issues in Exact Gravitational Lensing

The gravitational lensing problem is discussed in an exact setting - namely, without the use of approximations such as weak fields or thin lenses. In particular, the distortion of the images of elliptical sources is described in terms of three parameters (the semiaxes ratio, the area and orientation of the ellipse), and evolution equations for these parameters are derived. The evolution equations determine the image's shape from the source's shape, which acts as inital data, or viceversa. The evolution equations are first-order, nonlinear coupled ordinary differential equations for the three parameters, in which the divergence and shear of the past lightcone of the observer act as known sources. The deflector is encoded in the divergence and shear of the past lightcone of the observer by means of the optical equations.