Asymptotic structure at timelike infinity: higher orders

TL;DR

This paper investigates the detailed asymptotic structure of four-dimensional spacetimes at timelike infinity under the assumption of asymptotic stationarity, revealing restrictions on the metric form without requiring extra symmetries.

Contribution

It systematically analyzes higher-order asymptotic structures at timelike infinity in stationary spacetimes, highlighting deviations from Kerr black holes without additional symmetry assumptions.

Findings

Asymptotic stationarity imposes strong restrictions on the structure at timelike infinity.

The asymptotic form of the metric deviates from Kerr black holes.

No extra asymptotic symmetries are assumed in the analysis.

Abstract

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.