  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.
