Spurious Radial Migration from Relativistic Effects in the Milky-Way Disk

The gradient of the gravitational redshift in the potential of the Milky-Way induces an apparent spurious radial migration. I show that this effect is simply related to the local acceleration, which was measured recently by Gaia eDR3, implying a spectroscopic shift of $[-2.4x10^{-2}/(r/8kpc)] km/s/kpc. The transverse Doppler effect yields a comparable contribution. The spurious radial velocity from both relativistic effects amounts to crossing a major portion of the Milky-Way disk during the age of the universe, and must be corrected for in any future measurement of the actual radial migration of stars.