Boson stars and black holes with wavy scalar hair

TL;DR

This paper introduces a new type of scalar hair in boson stars and black holes characterized by spatial oscillations, which could lead to observable features like stable photon spheres and altered interior singularities.

Contribution

It demonstrates the existence of boson stars and black holes with wavy scalar hair, revealing new oscillatory features and potential observational signatures in space-time.

Findings

Scalar hair exhibits spatial oscillations away from the core or horizon.

Effective potential indicates possible stable photon spheres.

Black hole singularity occurs at finite radius close to the center.

Abstract

In this paper, we follow up on the discovery of a new type of solution in the Einstein-Maxwell system coupled minimally to a self-interacting complex scalar field. For sufficiently large gravitational coupling and sufficiently small electromagnetic coupling we demonstrate that boson stars as well as black holes can carry scalar hair that shows a distinct new feature~: a number of spatial oscillations in the scalar field away from the core or horizon, respectively. These spatial oscillations appear also in the curvature invariants and hence should be a detectable feature of the space-time. As a first hint that this is true, we show that the effective potential for null geodesics in this space-time possesses a local minimum indicating that in the spatial region where oscillations occur a new stable photon sphere should be possible. We also study the interior of the black holes with scalar hair and show that the curvature singularity appears at a finite value of the radius and that black holes with wavy scalar hair have this singularity very close to the center.