A perturbative no-hair of form fields for higher dimensional static black holes

TL;DR

This paper investigates the static perturbations of p-form fields around higher dimensional Schwarzschild black holes, demonstrating that such perturbations do not exist for p≥3, thus supporting the no-hair theorem for these fields.

Contribution

It provides a proof that static p-form field perturbations are absent for p≥3 in higher dimensional Schwarzschild spacetimes, reinforcing the no-hair property.

Findings

Static perturbations do not exist for p≥3.

Supports the no-hair theorem for higher-dimensional black holes.

Non-spherical black objects may still exist.

Abstract

In this paper we examine the static perturbation of p-form field strengths around higher dimensional Schwarzschild spacetimes. As a result, we can see that the static perturbations do not exist when p\geq 3. This result supports the no-hair properties of p-form fields. However, this does not exclude the presence of the black objects having non-spherical topology.