Asymptotically Schwarzschild spacetimes

It is shown that if an asymptotically flat spacetime is asymptotically stationary, in the sense that $£ξgab$ vanishes at the rate $∼t−3$ for asymptotically timelike vector field $ξa,$ and the energy-momentum tensor vanishes at the rate $∼t−4,$ then the spacetime is an asymptotically Schwarzschild spacetime.