# Hair loss in parity violating gravity

## TL;DR

This paper proves that in certain parity-violating gravity theories, non-spinning black holes cannot have scalar hair, affecting how gravitational wave observations constrain such theories.

## Contribution

It provides a mathematical proof that scalar hair is not sourced in vacuum, spherically symmetric spacetimes in parity-violating gravity extensions like dynamical Chern-Simons theory.

## Key findings

- Scalar hair is not sourced in non-spinning black holes within these theories.
- Observations of non-spinning black holes cannot constrain parity violation in gravity.
- Spinning black holes may still exhibit scalar hair, affecting observational tests.

## Abstract

The recent detection of gravitational waves by the LIGO/VIRGO collaboration has allowed for the first tests of Einstein's theory in the extreme gravity regime, where the gravitational interaction is simultaneously strong, non-linear and dynamical. One such test concerns the rate at which the binaries inspiral, or equivalently the rate at which the gravitational wave frequency increases, which can constrain the existence of hairy black holes. This is because black holes with scalar hair typically excite dipole radiation, which in turn leads to a faster decay rate and frequency chirping. In this paper, we present a mathematical proof that scalar hair is not sourced in vacuum, spherically symmetric spacetimes when considering extensions of Einstein's theory that break parity in gravity, focusing on dynamical Chern-Simons theory as a particular toy model. This result implies that the observational confirmation of the baldness of black holes cannot be used to constrain parity violation in gravity, unless the black holes observed are also spinning.