The cosmic distance duality relation with strong lensing and
  gravitational waves: an opacity-free test
  The cosmic distance duality relation (CDDR) is a fundamental assumption in
cosmological studies. Given the redshift $z$, it relates luminosity distance
$D^L$ with angular diameter distance $D^A$ through $(1+z)^2D^A/D^L\equiv1$.
Many efforts have been devoted to test the CDDR with various observational
approaches. However, to the best of our knowledge, those methods are always
affected by cosmic opacity which could make the CDDR violated due to the
non-conservation of photon number. Such mechanism is more related with
astropartical physics. In this work, to directly study the nature of
space-time, i.e., to disentangle it from astropartical physics, we propose a
new strategy to test the CDDR with strong lensing providing $D^A$ and
gravitational wave providing $D^L$. It is known that the propagation of
gravitational wave is unaffected by cosmic opacity. We demonstrate distances
from optical lensing observation are also opacity-free. These two kinds of
distance measurements make it possible to test any metric theories of gravity
where photons travel along null geodesics. Our results show the constraints on
deviations of the CDDR will be very competitive to current techniques.
