Axion boson stars with wormhole topology

TL;DR

This work constructs and analyzes a spherically symmetric, asymptotically flat configuration in four-dimensional gravity sourced by a phantom field and an axion scalar with a QCD-inspired potential, forming an Ellis-type wormhole at the core of an axion star. The model is controlled by the decay constant $f_a$, the axion frequency $\omega$, and the throat parameter $r_0$, and its properties are obtained by solving a coupled system of ODEs for the metric functions and scalar profiles, with key quantities including the ADM mass $M$, Noether charge $Q$, and phantom charge $\cal D$. The authors investigate traversability via the Kretschmann scalar and energy conditions, reveal topology changes (single to double throat) in embedding diagrams, and analyze null geodesics to characterize light rings, finding at least one unstable light ring at the throat and, in some regimes, multiple rings. These results illuminate how dark-sector fields interact in extreme gravity to produce rich wormhole–star configurations with potential observational signatures in photon orbits and lensing, while also highlighting the need for full dynamical stability analyses. $f_a$, $\omega$, and $r_0$ play pivotal roles in shaping the spacetime geometry, energy conditions, and the spectrum of photon orbits through their influence on the matter content and the spacetime curvature.

Abstract

We investigate a novel gravitational configuration formed by a massless real phantom field and an axion scalar field, minimally coupled to gravity. This system describes an Ellis-type wormhole situated at the center of an axion star. By normalizing the mass of the axion field to unity, the physical properties of the model are determined by three independent parameters: the potential's decay constant, the frequency of the axion field, and the wormhole's throat parameter. We assess the traversability of this wormhole by examining the curvature scalars and energy conditions of the static solution. Our analysis of the wormhole's embedding diagrams indicates that, although the wormhole typically exhibits a single-throat geometry, a double-throat configuration featuring an equatorial plane may arise under specific conditions. Finally, an analysis of the null-geodesics reveals the existence of at least one unstable light ring at the wormhole throat.

Figures (7)

• Figure 1: The ADM mass $M$ and Noether charge $Q$ as the function of frequency $\omega$ for some values of $f_a$ under $r_0 = 0.0001, 0.1, 0.5, 0.8$, the solid line represents $M$, and the dashed line represents $Q$.
• Figure 2: The Kretschmann scalar vs. radial coordinate $x$ under different values of $r_0$ and $f_a$.
• Figure 3: The phantom field scalar charge $\cal D$ vs. field frequency $\omega$ under different values of $r_0$ and $f_a$.
• Figure 4: Energy density $\rho$ and the sum of energy density and radial pressure $\rho+p_r$ for various throat parameters $r_0$ and frequency $\omega$.
• Figure 5: Two-dimensional view of the isometric embedding of the equatorial plane and the corresponding 3D embedding diagrams of wormhole solutions for different $f_a$ and $\omega$ with $r_0 = 0.1$ in the left, and $r_0 = 0.5, 0.8$ with different $f_a$ and $\omega$ on the right.