Lensing Degeneracies Revisited

This paper shows that the mass-sheet degeneracy and other degeneracies in lensing have simple geometrical interpretations: they are mostly rescalings of the arrival-time surface. Different degeneracies appear in Local Group lensing and in cosmological lensing, because in the former the absolute magnification is measured but the image structure is not resolved, whereas in the latter the reverse usually applies. The most dangerous of these is a combination we may call the `mass-disk degeneracy' in multiply-imaging galaxy lenses, which may lead to large systematic uncertainties in estimates of cosmological parameters from these systems.