Note on black hole no hair theorems for massive forms and spin-1/2 fields

TL;DR

This paper proves non-perturbative no hair theorems for massive 2-form fields and discusses perturbative no hair theorems for massive spin-1/2 fields across various black hole spacetimes in arbitrary dimensions.

Contribution

It provides a non-perturbative proof for massive 2-form fields and extends the analysis of spin-1/2 fields, broadening the understanding of black hole no hair theorems in diverse geometries.

Findings

Non-perturbative no hair theorem for massive 2-form fields in general spacetimes.

Perturbative no hair theorem for massive spin-1/2 fields in static backgrounds.

Discussion on generalization to higher form fields and other spacetime geometries.

Abstract

We give a proof of the non-perturbative no hair theorems for a massive 2-form field with 3-form field strength for general stationary axisymmetric and static (anti)-de Sitter or asymptotically flat black hole spacetimes with some suitable geometrical properties. The generalization of this result for higher form fields is discussed. Next, we discuss the perturbative no hair theorems for massive spin-1/2 fields for general static backgrounds with electric or magnetic charge. Some generalization of this result for stationary axisymmetric spacetimes are also discussed. All calculations are done in arbitrary spacetime dimensions.