Is the Schwarzschild black hole really stable?

TL;DR

This paper investigates the stability of the Schwarzschild black hole, focusing on odd perturbations, and finds that the white-hole-connected universe is unstable under these perturbations, especially related to rotation.

Contribution

It reexamines odd perturbations using Painlevé coordinates and suggests the white-hole-connected universe is unstable, highlighting the potential impact of rotational perturbations.

Findings

White-hole-connected universe is unstable under odd perturbations.

The instability may be related to rotational (angular) perturbations.

Reconsideration of perturbation analysis using Painlevé coordinates.

Abstract

The stability of the Schwarzschild black hole is studied. Regge and Wheeler treated the problem first at 1957 and obtained the dynamical equations for the small perturbation. There are two kinds of perturbations: odd one and even one. Using the Painlev\'{e} coordinate, we reconsider the odd perturbation and find that: the white-hole-connected universe(r>2m, see text) is unstable. Because the odd perturbation may be regarded as the angular perturbation, therefore, the physical mean to it may be that the white-hole-connected universe is unstable with respect to the rotating perturbation.