Calibration of gamma-ray bursts luminosity correlations using
  gravitational waves as standard sirens
  Gamma-ray bursts (GRBs) are a potential tool to probe high-redshift universe.
However, the circularity problem enforces people to find model-independent
methods to study the luminosity correlations of GRBs. Here, we present a new
method which uses gravitational waves as standard sirens to calibrate GRB
luminosity correlations. For the third-generation ground-based GW detectors
(i.e., Einstein Telescope), the redshifts of gravitational wave (GW) events
accompanied electromagnetic counterparts can reach out to $\sim 4$, which is
more distant than type Ia supernovae ($z\lesssim 2$). The Amati relation and
Ghirlanda relation are calibrated using mock GW catalogue from Einstein
Telescope. We find that the $1\sigma$ uncertainty of intercepts and slopes of
these correlations can be constrained to less than 0.2\% and 8\% respectively.
Using calibrated correlations, the evolution of dark energy equation of state
can be tightly measured, which is important for discriminating dark energy
models.
