---
title: "Spinning black holes and boson clouds"
description: "Why a spinning black hole can amplify a wave, how a trapped light field grows into a cloud, and how to recompute and read the results."
canonical_url: "https://sandboxphysics.com/stories/black-hole-superradiance/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/black-hole-superradiance/"
last_modified: "2026-11-14"
---

# Spinning black holes and boson clouds

Sandbox Physics · 2026-11-12

A spinning black hole can hand some of its rotational energy to a wave that circles it more slowly than its horizon turns. Start with that picture, work through the units and the conserved flux, recompute a published table yourself, and then read how a frontier paper turns growing clouds into limits on new particles.

[Open the black hole superradiance Lab](https://sandboxphysics.com/labs/black-hole-superradiance/)

1. L1 · Concept

   ## [Why can a spinning black hole make the waves around it ever stronger?](https://sandboxphysics.com/stories/black-hole-superradiance/why-a-spinning-black-hole-amplifies-waves/)

   A wave that circles a spinning black hole more slowly than its horizon turns comes back stronger, paid for by the hole's rotation.

2. L1 · Chapter

   ## [Waves, spin and the scales of a Kerr black hole](https://sandboxphysics.com/stories/black-hole-superradiance/waves-spin-and-kerr-scales/)

   Set up the units, horizon, horizon rotation and wave angular momentum, then derive when a wave can gain energy and when a light field is trapped.

3. L2 · Chapter

   ## [Conserved flux, physical units and a first growth estimate](https://sandboxphysics.com/stories/black-hole-superradiance/flux-units-and-a-first-growth-estimate/)

   Use the conserved wave flux to prove the gain condition, convert geometric units to seconds and electronvolts, and estimate a cloud's growth rate.

4. L3 · Chapter

   ## [Solving for the bound cloud's growth rate reproducibly](https://sandboxphysics.com/stories/black-hole-superradiance/solving-the-bound-cloud-reproducibly/)

   Find the cloud's complex frequency with a continued fraction, test convergence, avoid converging to the wrong overtone, and compare with a published table.

5. L3 · Method

   ## [Recomputing a published superradiance amplification table](https://sandboxphysics.com/stories/black-hole-superradiance/recomputing-a-published-amplification-table/)

   Download the authors' scalar amplification table, recompute the spin 0.99 slice with an independent solver, and see where the hydrogenic growth formula holds.

6. L3 · Paper guide

   ## [How self-interactions change boson-cloud limits from spins and gravitational waves](https://sandboxphysics.com/stories/black-hole-superradiance/reading-self-interacting-boson-cloud-limits/)

   Read Baryakhtar et al. 2021 figure by figure: which spin limits rest on measurements, which wave signals are projections, and what is still open.