Image Properties of Embedded Lenses
  We give analytic expressions for image properties of objects seen around
point mass lenses embedded in a flat $\Lambda$CDM universe. An embedded lens in
an otherwise homogeneous universe offers a more realistic representation of the
lens's gravity field and its associated deflection properties than does the
conventional linear superposition theory. Embedding reduces the range of the
gravitational force acting on passing light beams thus altering all quantities
such as deflection angles, amplifications, shears and Einstein ring sizes.
Embedding also exhibits the explicit effect of the cosmological constant on
these same lensing quantities. In this paper we present these new results and
demonstrate how they can be used. The effects of embedding on image properties,
although small i.e., usually less than a fraction of a percent, have a more
pronounced effect on image distortions in weak lensing where the effects can be
larger than 10%. Embedding also introduces a negative surface mass density for
both weak and strong lensing, a quantity altogether absent in conventional
Schwarzschild lensing. In strong lensing we find only one additional quantity,
the potential part of the time delay, which differs from conventional lensing
by as much as 4%, in agreement with our previous numerical estimates.
