# Challenges testing the no-hair theorem with gravitational waves

## TL;DR

This paper examines how gravitational wave measurements of black hole ringdowns test the no-hair theorem, revealing that increased signal strength does not always lead to tighter constraints on black hole parameters.

## Contribution

It introduces a framework for understanding how ringdown parameter constraints scale with signal loudness, considering the physical requirement for the remnant to settle into a Kerr-like state.

## Key findings

- Confidence intervals do not necessarily shrink with louder signals.
- More sensitive measurements can probe later times without tighter parameter constraints.
- Preliminary analysis suggests this effect is not due to numerical relativity artifacts.

## Abstract

General relativity's no-hair theorem states that isolated astrophysical black holes are described by only two numbers: mass and spin. As a consequence, there are strict relationships between the frequency and damping time of the different modes of a perturbed Kerr black hole. Testing the no-hair theorem has been a longstanding goal of gravitational-wave astronomy. The recent detection of gravitational waves from black hole mergers would seem to make such tests imminent. We investigate how constraints on black hole ringdown parameters scale with the loudness of the ringdown signal---subject to the constraint that the post-merger remnant must be allowed to settle into a perturbative, Kerr-like state. In particular, we require that---for a given detector---the gravitational waveform predicted by numerical relativity is indistinguishable from an exponentially damped sine after time $t^\text{cut}$. By requiring the post-merger remnant to settle into such a perturbative state, we find that confidence intervals for ringdown parameters do not necessarily shrink with louder signals. In at least some cases, more sensitive measurements probe later times without necessarily providing tighter constraints on ringdown frequencies and damping times. Preliminary investigations are unable to explain this result in terms of a numerical relativity artifact.