Uniqueness of Extremal Kerr and Kerr-Newman Black Holes

TL;DR

This paper proves that the only four-dimensional, stationary, rotating, asymptotically flat vacuum black hole with a single degenerate horizon is the extremal Kerr solution, and similarly for extremal Kerr-Newman black holes, completing a key aspect of black hole uniqueness theorems.

Contribution

It establishes the uniqueness of extremal Kerr and Kerr-Newman black holes among stationary, rotating, asymptotically flat solutions with a degenerate horizon.

Findings

Proves extremal Kerr is the unique solution under specified conditions.

Proves extremal Kerr-Newman is the unique solution under specified conditions.

Closes a longstanding gap in black hole uniqueness theorems.

Abstract

We prove that the only four dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a longstanding gap in the black hole uniqueness theorems.