# Kerr black holes with synchronised hair: an analytic model and dynamical formation

## TL;DR

This paper introduces an analytic model for Kerr black holes with synchronised Proca hair, validated against numerical simulations, and explores their formation via superradiance, enhancing understanding of hairy black hole states.

## Contribution

It presents a universal analytic model for Kerr black holes with synchronised hair, applicable in the weak hair regime, and compares it with numerical solutions to confirm accuracy.

## Key findings

- The model accurately describes hairy black holes with quasi-Kerr horizons.
- Numerical simulations confirm the model's validity in the superradiant domain.
- The study identifies conditions for the dynamical emergence of hairy black holes.

## Abstract

East and Pretorius (arXiv:1704.04791) have successfully evolved, using fully non-linear numerical simulations, the superradiant instability of the Kerr black hole (BH) triggered by a massive, complex vector field. Evolutions terminate in stationary states of a vector field condensate synchronised with a rotating BH horizon. We show these end points are fundamental states of Kerr BHs with synchronised Proca hair. Motivated by the "experimental data" from these simulations we suggest a universal (i.e. field-spin independent), analytic model for the subset of BHs with sychronised hair that possess a quasi-Kerr horizon, applicable in the weak hair regime. Comparing this model with fully non-linear numerical solutions of BHs with synchronised scalar or Proca hair, we show the model is accurate for hairy BHs that may emerge dynamically from superradiance, whose domain we identify.