Test of the second postulate of relativity from gravitational wave observations

The second postulate of special relativity states that the speed of light in vacuum is independent of the emitter's motion. Though this claim has been verified in various experiments and observations involving electromagnetic radiation with very high accuracy, such a test for gravitational radiation still needs to be explored. We analyzed data from the LIGO and Virgo detectors to test this postulate for gravitational radiation within the ambit of \textit{emission models}, where the speed of gravitational waves emitted by a source moving with a velocity v relative to a stationary observer is given by c'=c+kv, where k is a constant. We have estimated the upper bound on the 90\% credible interval over k that parameterizes the deviation from the second postulate to be k≤8.3×10−18 which is several orders of magnitude more stringent compared to previous bounds obtained from electromagnetic observations. The Bayes' factor supports the second postulate, with very strong evidence that the data is consistent with the null hypothesis k=0. This confirms that the speed of gravity is independent of the motion of the emitter, upholding the principle of relativity for gravitational interactions.