Uniqueness of the Axionic Kerr Black Hole

TL;DR

This paper proves that the axionic Kerr black hole is the unique stationary solution within a specific gravity and field theory framework, characterized by regularity, asymptotic flatness, and finite axion field strength.

Contribution

It establishes the uniqueness of the axionic Kerr black hole as a stationary solution under certain symmetry and invariance conditions.

Findings

Proves the axionic Kerr black hole's uniqueness as a stationary solution.

Shows the solution has a regular event horizon and is asymptotically flat.

Demonstrates finite axion field strength at the horizon.

Abstract

Under the axisymmetry and under the invarance of simultaneous inversion of time and azimuthal angle, we show that the axionic Kerr black hole is the ${\it unique}$ stationary solution of the minimal coupling theory of gravity and the Kalb-Ramond field, which has a regular event horizon, is asymptotically flat and has a finite axion field strength at event horizon.