Using gravitational wave to test general relativity

The first direct detection of gravitational wave was realized by LIGO on September 14, 2015. Since then gravitational wave detection progresses very rapidly. So far, LIGO has confirmed 5 gravitational wave events of binary black hole merger, including GW150914, GW151226, GW170608, GW170104 and GW170814. And one gravitational wave event of binary neutron star merger has also been detected very recently, GW170817. Besides these 6 gravitational events LIGO has one more suspected gravitational wave event of binary black hole merger LVT151012. Inspired by the gravitational wave detection, gravitational wave physics and gravitational wave astronomy develop also very rapidly since 2016. The direct detection of gravitational wave qualitatively supports the general theory of relativity. But gravitational wave detection, as experiments involving strong gravitational field and strongly dynamical space-time region, can also quantitatively tests general relativity, and even find the applicable scope of general relativity, and point out the development of gravity theory beyond general relativity. In this paper, we will introduce how to use gravitational wave to test general relativity. We will try to give a comprehensive introduction to the possible ways applying gravitational wave detection to test general relativity, including the qualitative properties of gravitational waves, the degree of freedom of gravitational waves, the speed of gravitational wave propagation and the waveform characteristics of gravitational waves.