No-dipole-hair theorem for higher-dimensional static black holes

TL;DR

This paper proves that higher-dimensional static black holes cannot have non-trivial electric p-form fields within a certain range, implying they cannot support dipole hair under these fields.

Contribution

It establishes a no-dipole-hair theorem for static black holes in higher dimensions with specific electric p-form fields, extending previous results.

Findings

Static black holes cannot support non-trivial electric p-form fields for (n+1)/2 <= p <= n-1.

Higher-dimensional static black holes lack dipole hair under these fields.

The theorem applies to asymptotically flat spacetimes.

Abstract

We prove that static black holes in n-dimensional asymptotically flat spacetime cannot support non-trivial electric p-form field strengths when (n+1)/2<= p <= n-1. This implies in particular that static black holes cannot possess dipole hair under these fields.