# Kerr black holes with parity-odd scalar hair

## TL;DR

This paper investigates Kerr black holes with parity-odd scalar hair, revealing new solutions with unique ergoregion topologies and expanding understanding of scalar field configurations around rotating black holes.

## Contribution

It introduces parity-odd scalar hair in Kerr black holes, demonstrating their properties, existence domain, and novel ergoregion structures in four-dimensional spacetime.

## Key findings

- Existence of parity-odd hairy Kerr black holes
- Discovery of new composite ergosurfaces with double-torus topology
- Characterization of scalar hair properties and solution domain

## Abstract

We study Kerr black holes with synchronised non-trivial parity-odd massive scalar hair in four dimensional asymptotically flat space-time. These axially symmetric stationary spinning solutions of the minimally coupled Einstein-Klein-Gordon theory provide yet another example of bound states in synchronous rotation with the event horizon. We discuss the properties of these parity-odd hairy black holes and boson stars and exhibit their domain of existence. Considering the ergo-regions of these hairy black holes, we show that apart from the previously discussed ergo-sphere and ergo-Saturn, they support a new type of composite ergo-surfaces with the topology of a double-torus-Saturn $(S^1\times S^1)\bigoplus(S^1\times S^1)\bigoplus S^2$.