On Newman-Penrose constants of stationary space-times

We consider the general asymptotic expression of stationary space-time. Using Killing equation, we reduce the dynamical freedom of Einstein equation to the in-going gravitational wave ${\mathrm{\Psi }}_0$. The general form of this function can be got. With the help of asymptotically algebraic special condition, we prove that all Newman-Penrose constants vanish.