Strong lensing as a giant telescope to localize the host galaxy of
  gravitational wave event
  Standard siren cosmology of gravitational wave (GW) merger events relies on
the identification of host galaxies and their redshifts. But this can be highly
challenging due to numerous candidates of galaxies in the GW localization area.
We point out that the number of candidates can be reduced by orders of
magnitude for strongly lensed GW events, due to extra observational
constraints. For the next-generation GW detectors like Einstein Telescope (ET),
we estimate that this number is usually significantly less than one, as long as
the GW localization uncertainty is better than $\sim 10\, \rm deg^2$. This
implies that the unique identification of the host galaxy of lensed GW event
detected by ET and Cosmic Explorer (CE) is possible. This provides us a
promising opportunity to measure the redshift of the GW event and facilitate
the standard siren cosmology. We also discuss its potential applications in
understanding the evolution process and environment of the GW event.
