Asymptotic Schwarzschild Spacetimes

TL;DR

This paper demonstrates that under specific decay conditions of the metric and energy-momentum tensor, an asymptotically flat and stationary spacetime must be asymptotically Schwarzschild, offering new insights into black hole uniqueness.

Contribution

It establishes a new asymptotic characterization of Schwarzschild spacetimes based on decay rates of the metric and energy-momentum tensor.

Findings

Spacetime is asymptotically Schwarzschild under given conditions

Provides a new perspective on black hole uniqueness

Connects decay rates to spacetime classification

Abstract

It is shown that if an asymptotically flat spacetime is asymptotically stationary, in the sense that $\Lie_{\xi} g_{ab}$ vanishes at the rate $\sim t^{-3}$ for asymptotically timelike vector field $\xi^a$, and the energy-momentum tensor vanishes at the rate $\sim t^{-4}$, then the spacetime is an asymptotically Schwarzschild spacetime. This gives a new aspect of the uniqueness theorem of a black hole.