The geometry of gravitational lensing magnification
  We present a definition of unsigned magnification in gravitational lensing
valid on arbitrary convex normal neighborhoods of time oriented Lorentzian
manifolds. This definition is a function defined at any two points along a null
geodesic that lie in a convex normal neighborhood, and foregoes the usual
notions of lens and source planes in gravitational lensing. Rather, it makes
essential use of the van Vleck determinant, which we present via the
exponential map, and Etherington's definition of luminosity distance for
arbitrary spacetimes. We then specialize our definition to spacetimes, like
Schwarzschild's, in which the lens is compact and isolated, and show that our
magnification function is monotonically increasing along any geodesic contained
within a convex normal neighborhood.
