# On long range axion hairs for black holes

## TL;DR

This paper explores how Chern-Simons axion couplings can produce long-range axion fields around charged black holes, extending known solutions and analyzing their physical effects, including light deflection and orbital properties.

## Contribution

It introduces new analytical solutions for axion hairs around charged black holes with non-minimal couplings, expanding understanding of black hole-axion interactions.

## Key findings

- Axion profiles depend on black hole charges and influence horizon properties.
- Derived a Smarr formula for these axion-coupled black hole solutions.
- Studied phenomenological effects like light deflection and ISCO modifications.

## Abstract

The physics of black holes can suggest new ways to test the existence of axions. Much work has been done so far to analyse the phenomenon of superradiance associated with axions in the ergoregion surrounding rotating black holes. In this work, we instead investigate how Chern-Simons axion couplings of the form $\phi \,F\,\tilde F$ and $\phi \,R\,\tilde R$, well motivated by particle physics and string theory, can induce long range profiles for light axion fields around charged black holes, with or without spin. We extend known solutions describing axion hairs around spherically symmetric, asymptotically flat dyonic black hole configurations, charged under $U(1)$ gauge symmetries, by including non-minimal couplings with gravity. The axion acquires a profile controlled by the black hole conserved charges, and we analytically determine how it influences the black hole horizon and its properties. We find a Smarr formula applying to our configurations. We then generalise known solutions describing axion hairs around slowly rotating black hole configurations with charge. To make contact with phenomenology, we briefly study how long range axion profiles induce polarised deflection of light rays, and the properties of ISCOs for the black hole configurations we investigate.