Asymptotically Schwarzschild space-times

It is shown that if an asymptotically flat space-time is asymptotically sta tionary, in the sense that L(xi)g(ab) vanishes at the rate similar to t(-3) for asymptotically timelike vector field xi(a), and the energy-momentum te nsor vanishes at the rate similar to t(-4), then the space-time is an asymp totically Schwarzschild space-time. This gives a new aspect of the uniquene ss theorem of a black hole. (C) 1999 American Institute of Physics. [S0022- 2488(99)00704-5].