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Bulk flow velocities are typically estimated in the idealised picture whereobservers are moving within a perfectly homogeneous and isotropic space-time.This picture is consistent within standard perturbation theory up torelativistic effects that lead to correction terms of order $v z$, where $z$ isthe redshift of observation, and $v$ is the amplitude of the bulk flow. Thedominant relativistic contributions at scales $z \lesssim 1$ are caused bygravitational redshift and time evolution of the velocity field. We includethese effects within a broadly applicable weak-field approximation, and providea cosmographic formula for estimating bulk flows at a high precision. Based onthis formula, we judge that recent bulk flow estimates are biased toward largervalues by $\sim 10\%$. This theoretical bias surpasses the measurement biasesof the same estimates, and it will become still more important to account forthe relativistic effects as the scales at which bulk flows are estimated toincrease.

Bulk flows in the local Universe and the importance of relativistic effects