Pi from the sky -- A null test of general relativity from a population of gravitational wave observations

Our understanding of observed Gravitational Waves (GWs) comes from matching data to known signal models describing General Relativity (GR). These models, expressed in the post-Newtonian formalism, contain the mathematical constant $\pi$. Allowing $\pi$ to vary thus enables a strong, universal and generalisable null test of GR. From a population of 22 GW observations, we make an astrophysical measurement of $\pi=3.115^{+0.048}_{-0.088}$, and prefer GR as the correct theory of gravity with a Bayes factor of 321. We find the variable $\pi$ test robust against simulated beyond-GR effects.