A new method to test the cosmic distance duality relation using the
  strongly lensed gravitational waves
  We propose a new method to test the cosmic distance duality relation using
the strongly lensed gravitational waves. The simultaneous observations of image
positions, the relative time delay between different images, the redshift
measurements of lens and source, together with the mass modelling of the lens
galaxy, provide the angular diameter distance to the gravitational wave source.
On the other hand, from the observation of gravitational wave signals the
luminosity distance to the source can be obtained. This is to our knowledge the
first method to simultaneously measure both the angular diameter distance and
luminosity distance from the same source. Thus, the strongly lensed
gravitational waves provide a unique way to test the cosmic distance duality
relation. With the construction of the third generation gravitational detectors
such as the Einstein Telescope in the future, it is possible to test the cosmic
distance duality relation at an accuracy of several percent.
