# Uniqueness of Kerr-Newman-de Sitter black holes with small angular momenta

## TL;DR

This paper proves that stationary solutions near a Reissner-Nordström-de Sitter black hole are actually Kerr-Newman-de Sitter solutions with small angular momentum, using stability and extension arguments without requiring analyticity.

## Contribution

It establishes a uniqueness theorem for Kerr-Newman-de Sitter black holes with small angular momenta, removing the need for analyticity assumptions.

## Key findings

- Stationary solutions close to Reissner-Nordström-de Sitter are Kerr-Newman-de Sitter.
- The proof leverages recent stability results for small angular momenta.
- No analyticity assumptions are needed for the uniqueness result.

## Abstract

We show that a stationary solution of the Einstein-Maxwell equations which is close to a non-degenerate Reissner-Nordstr\"om-de Sitter solution is in fact equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the non-linear stability of the Kerr-Newman-de Sitter family of black holes for small angular momenta, recently established by the author, together with an extension argument for Killing vector fields. Our black hole uniqueness result only requires the solution to have high but finite regularity; in particular, we do not make any analyticity assumptions.