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Related Experiment Video

Updated: May 5, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Linear Stability of the Slowly-Rotating Kerr-de Sitter Family.

Allen Juntao Fang¹

¹Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 Place Jussieu, Paris, 75005 Île-de-France France.

Annals of PDE

|May 4, 2026

Summary

This study proves the linear stability of slowly-rotating Kerr-de Sitter black holes. The findings offer a novel approach to nonlinear stability using spectral gap analysis and vectorfield methods.

Keywords:

Black hole stability General relativity Harmonic coordinates Wave equation

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Area of Science:

General Relativity
Mathematical Physics
Black Hole Physics

Background:

The Kerr-de Sitter family represents solutions to Einstein's vacuum equations with positive cosmological constant.
Understanding the stability of these black hole solutions is crucial for theoretical physics.

Purpose of the Study:

To prove the linear stability of the slowly-rotating Kerr-de Sitter black hole family.
To present a novel, self-contained approach to the nonlinear stability of these solutions.
To offer an alternative to existing proofs, avoiding specific mathematical techniques like b-calculus.

Main Methods:

Interpreting quasinormal modes as H^k eigenvalues on a Hilbert space.
Utilizing integrated local energy decay estimates to establish a spectral gap.
Employing standard pseudo-differential arguments near the trapped set and the vectorfield method.

Main Results:

Linear stability of the slowly-rotating Kerr-de Sitter black hole family is proven.
A spectral gap is demonstrated through integrated local energy decay estimates.
The vectorfield method is shown to yield resolvent estimates on a trapping background.

Conclusions:

The study provides a rigorous proof of linear stability for a significant class of black hole solutions.
The novel methodology offers a new perspective on nonlinear stability analysis in general relativity.
The work contributes to a deeper understanding of black hole dynamics in an expanding universe.