Asymptotic structure at timelike infinity: higher orders

Bearing the final fate of gravitational collapse in mind, we study the asymptotic structures at timelike infinity in four dimensions. Assuming that spacetimes are asymptotically stationary, we will examine the asymptotic structure of asymptotic stationary spacetimes in a systematic way. Then we see that the asymptotic stationarity strongly restricts the asymptotic structure at timelike infinity. We also observe that the resulted asymptotic form of the metric have the deviation from the Kerr black hole spacetime without assuming of the presence of some additional asymptotic symmetries.