What does a regular star look like?

TL;DR

This work investigates how regular, horizonless star spacetimes (exemplified by Hayward and Bardeen metrics) shape gravitational lensing and disk emission. By analyzing null geodesics and performing ray-tracing for geometrically thin/thick and optically thin disk models, the authors show that photons can pass through the center, creating a central bright spot, and that secondary images can be suppressed or disappear as the regularization parameter $\beta$ increases. These features—central transparency and incomplete secondary images—offer distinctive observational signatures to distinguish regular stars from black holes in future surveys. The findings have implications for identifying dark-matter–related compact objects and motivate further studies of regular spacetimes in astrophysical contexts.

Abstract

Recently, astronomers discovered unusual Einstein cross images of the galaxy HerS-3, which feature a bright central spot. Motivated by studies of images produced by regular stars, it has been proposed that optical appearances caused by compact stars acting as gravitational lenses may account for this central bright spot. We further suggest that images produced by regular stars exhibit additional characteristics distinct from those of ordinary black holes, such as the possible partial or complete absence of secondary images. These phenomena may serve as favorable observational criteria for identifying regular stars in future searches.

Figures (7)

• Figure 1: Null geodesics in the Hayward spacetime for different $\beta$ values, where the first row presents $r_m$ as a function of the impact parameter $b$, the second row presents the orbit number $n$ versus $b$ with green, orange, and red indicating the direct, lensed, and photon ring, respectively, and the third row displays the light trajectories for $b \in (0,10)$ using the same color scheme as the second row.
• Figure 2: Null geodesics in the Bardeen spacetime for various $\beta$ values, analogous to those shown in Fig.\ref{['fig:light_ray']}.
• Figure 3: Gravitational lensing induced by a transparent spacetime configuration described by the Hayward metric with $\beta=5$: the left panel shows an emitting disk of radius $2M$ located at $-100M$ (orange solid line), light rays propagating around the exterior of the spacetime structure (blue solid lines), and light rays traversing the interior of the structure (green solid lines), with the observer plane placed at $+\infty$; the corresponding lensed image on the observer plane is displayed in the right panel.
• Figure 4: Images of a geometrically and optically thin accretion disk for different values of $\beta$. The first row shows the dependence of the transfer function $r_{ts}$ on the impact parameter $b$, where green, orange, and red denote the distances to the first three intersection points between the light ray and the disk plane. The second row shows the radial dependence of the normalized emission intensity $I_{em}$. The third row displays the normalized observed intensity $I_{obs}$ as a function of $r$. The fourth row presents the resulting images of the geometrically and optically thin accretion disk.
• Figure 5: The coordinate system luminet_1979tian_2019.