  Similarly, an acceleration vector along the galaxy’s worldline determines whether the galaxy is accelerating. That acceleration vector is an invariant. So, if the galaxy in the left hand distribution has a zero acceleration vector, then the corresponding galaxy in the right hand distribution will also have a zero acceleration vector. Remember, a hole transformation preserves invariants. So if a galaxy is unaccelerated in the left hand distribution, it is also unaccelerated in the right hand distibution.