---
title: "Why can a spinning black hole make the waves around it ever stronger?"
description: "A wave that circles a spinning black hole more slowly than its horizon turns comes back stronger, paid for by the hole's rotation."
canonical_url: "https://sandboxphysics.com/stories/black-hole-superradiance/why-a-spinning-black-hole-amplifies-waves/"
language: "en"
page_type: "story"
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  zh-CN: "https://sandboxphysics.com/zh/stories/black-hole-superradiance/why-a-spinning-black-hole-amplifies-waves/"
last_modified: "2026-11-12"
---

[Spinning black holes and boson clouds](https://sandboxphysics.com/stories/black-hole-superradiance/)

# Why can a spinning black hole make the waves around it ever stronger?

Sandbox Physics · 2026-11-12

A spinning black hole can return a wave stronger than it arrived when the wave circles the hole more slowly than the hole's horizon turns. The extra energy comes out of the hole's rotation. If something keeps sending the wave back in, every pass adds a little more, and the wave grows.

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

## A wheel that speeds up waves

Picture a turntable covered in a material that soaks up sound. Play a tone towards it that swirls around the axis in the same sense as the turntable. If the turntable's rim moves faster than the swirling pattern of the sound, the absorbing surface does not slow the wave down. It drags it forward, and the reflected sound is louder than the sound that went in. The turntable slows slightly. It has paid for the extra sound with its own spin.

In 1971 Yakov Zel'dovich showed that this happens for any rotating, absorbing body. A wave pattern with $m$ crests around the axis and angular frequency $\omega$ turns at the rate $\omega/m$. If the body turns at rate $\Omega$, the reflected wave is amplified when

$$
\omega<m\Omega .
$$

The effect is called rotational superradiance. In 2017 a team of physicists measured it in a tank of water draining through a central hole: surface waves that co-rotated with the swirling flow came back amplified in a band of frequencies. [Brito, Cardoso and Pani, Superradiance, §1 and §4.10](https://arxiv.org/abs/1501.06570v8)

## A black hole has a spinning surface too

Nothing can climb back out of a black hole, so at first a black hole looks like the worst possible place to gain energy. But a spinning black hole drags space around with it, and its horizon turns at a definite rate, written $\Omega_H$. The horizon also absorbs whatever crosses it. That is all Zel'dovich's argument needs: a rotating surface that absorbs.

When a wave turns more slowly than the horizon, the part that falls in carries negative energy, as measured by a distant observer. Nothing escapes from inside. The hole simply loses rotational energy, and the reflected wave carries that energy away. A non-rotating hole has $\Omega_H=0$, so it can only absorb.

The effect is small for a single pass. For the fastest-spinning holes, the largest gain for a massless scalar wave is about 0.4 percent; for light it is about 4.4 percent, and for gravitational waves about 138 percent. [Brito, Cardoso and Pani, Superradiance, §4.7.3](https://arxiv.org/abs/1501.06570v8) We recomputed the scalar case ourselves: for a hole spinning at 99 percent of the maximum, a wave with $m=1$ gains 0.366 percent of its energy at the best frequency.

## Put a mirror around it

In 1972 William Press and Saul Teukolsky asked what happens if a mirror surrounds the hole. The amplified wave bounces back in, gains again and comes out stronger, over and over. They called the result a black-hole bomb. [Brito, Cardoso and Pani, Superradiance, §5.4.1](https://arxiv.org/abs/1501.06570v8)

Nature can supply the mirror. A particle with a small mass cannot escape from the hole's gravity if it moves slowly enough. Its wave is trapped in orbits that look like the electron states of a hydrogen atom, with the black hole as the nucleus. If the particle is a boson, any number of them can occupy the same state, so the trapped wave can grow into a huge cloud. Each pass near the horizon multiplies the cloud a little, and the growth becomes exponential.

The growth is fastest when the particle's wavelength is comparable to the hole's size. For a hole spinning at 99 percent of the maximum, the wave in the fastest-growing cloud grows by a factor of $e$ in about 6.7 million units of the hole's natural time, $GM/c^3$. [Dolan, Instability of the massive Klein-Gordon field on the Kerr spacetime, Table I](https://arxiv.org/abs/0705.2880v2) For a hole of ten solar masses that is about five and a half minutes. The particle would need a rest energy near $6\times10^{-12}$ electronvolts, about $10^{17}$ times lighter than an electron.

## Why astronomers care

A growing cloud takes its energy and angular momentum from the hole, so it spins the hole down until the cloud's frequency matches the horizon's rotation and the growth stops. If a very light particle of the right mass exists, old black holes should not spin fast. Measured black-hole spins, and the gravitational waves a cloud would emit, can therefore test ideas such as axion-like particles that are hard to reach in a laboratory.

These tests depend on more than the growth rate. A real particle may interact with itself, and a 2021 study by Masha Baryakhtar and colleagues found that strong self-interactions can stop a cloud from growing large, weakening both the spin-down and the gravitational-wave signal. [Baryakhtar, Galanis, Lasenby and Simon, Black hole superradiance of self-interacting scalar fields](https://arxiv.org/abs/2011.11646v2) No such cloud has been observed. What superradiance gives today is a way to ask whether such particles exist, using black holes as detectors.

## Try it in the Lab

Start from the amplified preset, then drag the spin dial back to zero and watch the gain turn negative. [Open the black hole superradiance Lab](https://sandboxphysics.com/labs/black-hole-superradiance/)

## Sources

1. [Brito, Cardoso and Pani, Superradiance, §1 and §4.10](https://arxiv.org/abs/1501.06570v8)
2. [Dolan, Instability of the massive Klein-Gordon field on the Kerr spacetime, Table I](https://arxiv.org/abs/0705.2880v2)
3. [Baryakhtar, Galanis, Lasenby and Simon, Black hole superradiance of self-interacting scalar fields](https://arxiv.org/abs/2011.11646v2)

## Keep reading

Spinning black holes and boson clouds · Reading path

### From an amplified wave to a growing cloud

1. [You are here **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/)
2. [Article **Waves, spin and the scales of a Kerr black hole**](https://sandboxphysics.com/stories/black-hole-superradiance/waves-spin-and-kerr-scales/)
3. [Article **Conserved flux, physical units and a first growth estimate**](https://sandboxphysics.com/stories/black-hole-superradiance/flux-units-and-a-first-growth-estimate/)
4. [Article **Solving for the bound cloud's growth rate reproducibly**](https://sandboxphysics.com/stories/black-hole-superradiance/solving-the-bound-cloud-reproducibly/)
5. [Article **Recomputing a published superradiance amplification table**](https://sandboxphysics.com/stories/black-hole-superradiance/recomputing-a-published-amplification-table/)
6. [Article **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/)