Hayward spacetime with axion scalar field

TL;DR

This paper explores Hayward axion stars, revealing extreme solutions with critical horizons, high concentration of scalar fields, and unique properties like frozen states and multiple light rings, using numerical methods.

Contribution

It introduces the concept of Hayward axion frozen stars, showing how magnetic charge influences their structure and properties, a novel insight into axion star configurations.

Findings

Existence of extreme solutions with critical horizons when magnetic charge exceeds a threshold.

Scalar field and energy density are highly concentrated within the horizon, with gravity nearly stopping time.

Frozen star solutions have two light rings whose positions depend on magnetic charge.

Abstract

In this work, we investigate a static spherically symmetric system in which Einstein gravity is minimally coupled with a self-interacting complex scalar field and a nonlinear electromagnetic field, referred to as Hayward axion stars. Employing numerical methods, we find that it essentially describes axion stars with the magnetic charge. In the absence of magnetic charge and with only the scalar field present, the system reduces to axion stars. We discover that when the magnetic charge $q$ exceeds a critical value, extreme solutions with frequencies $\omega$ approaching zero can be found and the critical horizon emerges. Within this horizon, the scalar field and energy density are highly concentrated and decrease precipitously at its boundary. The time component of the metric function approaches zero within this region, indicating that gravity is extremely intense, and time nearly ceases to flow. To an observer at infinity, the star appears to be frozen, hence we refer to these extreme solutions exhibiting a critical horizon as Hayward axion frozen stars. Furthermore, it is important to note that as $\omega \rightarrow 0$, the mass of the Hayward axion frozen star becomes independent of the decay constant and is only determined by the magnetic charge. Additionally, we find that the frozen star solutions possess two light rings. With an increase in the magnetic charge, these light rings move outward, while changes in the decay constant have little effect on their positions.