Late-time symmetry near black hole horizons

TL;DR

This paper demonstrates that late-time symmetries, specifically asymptotic Killing vectors, are present near black hole horizons and can extend outward, supporting the idea of black hole rigidity and symmetry at late times.

Contribution

It shows the existence and extension of asymptotic Killing vectors near black hole horizons, suggesting late-time symmetry and axisymmetry in rotating black holes.

Findings

Asymptotic Killing vectors exist at late times near horizons.

These vectors can be extended outside black holes under analyticity assumptions.

Rotating black holes may exhibit asymptotic axisymmetry at late times.

Abstract

It is expected that black holes are formed dynamically under the gravitational collapses and approach to the stationary states. In this paper, we show that the asymptotic Killing vector at late time should exist on the horizon and then that it can be extended to the out of black holes under the assumption of the analyticity of spacetimes. This fact implies that if there is another asymptotic Killing vector which becomes stationary Killing at far region and spacelike in "ergoregion", the rotating black holes may have the asymptotically axisymmetric Killing vector at late time. Thus, we may expect that the asymptotic rigidity of the black holes holds.