Testing the nature of gravitational-wave polarizations using strongly lensed signals

Gravitational-wave (GW) observations by a network of ground-based laser interferometric detectors allow us to probe the nature of GW polarizations. This would be an interesting test of general relativity, since general relativity predicts only two polarization modes while there are theories of gravity that predict up to six polarization modes. The ability of GW observations to probe the nature of polarizations is limited by the available number of linearly independent detectors in the network. (To extract all polarization modes, there should be at least as many detectors as the polarization modes.) Strong gravitational lensing of GWs offers a possibility to significantly increase the effective number of detectors in the network. Due to strong lensing (e.g., by galaxies), multiple copies of the same signal can be observed with time delays of several minutes to weeks. Owing to the rotation of the earth, observation of the multiple copies of the same GW signal would allow the network to measure different combinations of the same polarizations. This effectively multiplies the number of detectors in the network. Focusing on strongly lensed signals from binary black hole mergers that produce two observable ``images,'' using Bayesian model selection and assuming simple polarization models, we show that our ability to distinguish between polarization models is significantly improved.