On the waveforms of gravitationally lensed gravitational waves
  Strong lensing by intervening galaxies can produce multiple images of
gravitational waves from sources at cosmological distances. These images
acquire additional phase-shifts as the over-focused wavefront passes through
itself along the line of sight. Time domain waveforms of Type-II images
(associated with saddle points of the time delay) exhibit a non-trivial
distortion from the unlensed waveforms. This phenomenon is in addition to the
usual frequency-independent magnification, and happens even in the geometric
limit where the wavelength is much shorter than the deflector's gravitational
length scale. Similarly, Type-III images preserve the original waveform's shape
but exhibit a sign flip. We show that for non-precessing binaries undergoing
circular inspiral and merger, these distortions are equivalent to rotating the
line of sight about the normal to the orbital plane by $45^\circ$ (Type II) and
$90^\circ$ (Type III). This effect will enable us to distinguish between the
different topological types among a set of multiple images, and give us
valuable insight into the lens model. Furthermore, we show that for eccentric
binaries, the waveform of a Type-II image is distorted in a manner that is
inequivalent to a change of the source's orbital parameters.
