Shadows of rotating traversable wormholes surrounded by plasma

TL;DR

This paper investigates how a dispersive plasma environment alters the shadows of rotating traversable wormholes, using a separable Hamilton-Jacobi framework to obtain analytic shadow boundaries for several Teo-type spacetimes. By enforcing an separability condition for the plasma frequency via $\omega_p^2(r,\theta)=(f_r(r)+f_\theta(\theta))/(r^2K^2)$, the authors derive radial and angular equations $R(r)$ and $\Theta(\theta)$ and express the shadow boundary in terms of impact parameters $\xi$ and $\eta$, with the observer’s celestial coordinates computed from a ZAMO tetrad. They show that radial-only plasma profiles induce Kerr-like shadow evolution largely independent of the metric, while angular-dependent profiles yield metric-specific photon regions and forbidden regions, leading to observable differences between wormholes and Kerr black holes. The study identifies plasma-frequency–dependent critical values below which shadows exist; for all wormholes these critical frequencies are lower than Kerr’s in the same environment, producing plasma regimes where Kerr casts a shadow but wormholes do not, thereby offering a strong observational signature. Aberration due to observer motion further amplifies the differences, aiding potential detection of wormholes in realistic plasma environments.

Abstract

We study the influence of the plasma environment on the shadows of stationary axisymmetric wormholes. We consider a sample of several wormhole solutions and plasma distributions for which the Hamilton-Jacobi equation for the light rays is separable. This allows us to derive analytical expressions for the shadow boundary and examine the behavior of the photon regions as the plasma frequency varies. We observe that plasma profiles which depend only on radial coordinate lead to common evolution of the photon region which does not depend on the wormhole metric and is consistent with the Kerr black hole. For plasma profiles with angular dependence the evolution of the photon region is specific for every spacetime thus wormholes are observationally distinguishable. We further investigate the formation of forbidden regions in the plasma medium where light cannot propagate. They lead to the formation of plasma frequency ranges where the shadow is no longer observable and we show that this phenomenon is characteristic for all the configurations in our sample. We obtain the critical frequencies for which the shadow vanishes and demonstrate that for all the wormholes they are lower than the critical frequencies for the Kerr black hole in the same environment. This implies that there exist plasma frequency ranges in which the Kerr black hole casts a shadow but wormholes do not, creating a strong observational signature for discriminating between compact objects. In the frequency ranges where both black hole and wormhole shadows exist the wormhole shadows are consistently smaller than those for the Kerr black hole. As the plasma frequency grows the discrepancy progresses showing that plasma medium facilitates the experimental detection of wormholes. Finally we consider aberrational effects on the wormhole shadows. They further increase the deviation from black holes making wormholes easier to detect.

Figures (22)

• Figure 1: WH1 spacetime with plasma distribution $f_r = \omega{_c}{^2} \sqrt{m{^3}r}$, $f_{\theta} =0$, and spin parameter $a=0.999m$. The top-left panel corresponds to the frequency ratio $\omega{_c}/ \omega{_0} = 1$; the-top right to $\omega{_c}/ \omega{_0} = 2.7$, the bottom-left to $\omega{_c}/ \omega{_0} = 3.2$ and bottom-right has frequency $\omega{_c}/ \omega{_0} = 3.3$. The photon region is shown in orange, while the forbidden zone is indicated in grey. The forbidden region forms initially at the poles and subsequently expands toward the equatorial plane as the plasma frequency increases.
• Figure 2: Shadow of the Kerr black hole (left) compared to the shadow of WH1 spacetime (right) for plasma distribution $f_r = \omega{_c}{^2} \sqrt{m{^3}r}$, $f_{\theta}=0$, and spin parameter $a=0.999m$.
• Figure 3: WH2 spacetime with plasma distribution $f_r = 4\omega{_c}{^2}m{^2}\sqrt{m/r}$, $f_{\theta} =0$, and spin parameters $a=0.999m$. The top-left corresponds to the frequency ratio $\omega{_c}/ \omega{_0} = 1$; the top-right to $\omega{_c}/ \omega{_0} = 2.2$, the bottom-left to $\omega{_c}/ \omega{_0} = 2.6$ and the bottom-right to $\omega{_c}/ \omega{_0} = 3.2$. The forbidden zone forms first near the poles and gradually expands toward the equatorial plane as the plasma frequency increases.
• Figure 4: Shadow of the Kerr black hole (left) compared to the shadow of the WH2 spacetime (right) for plasma distribution $f_r = 4\omega{_c}{^2}m{^2}\sqrt{m/r}$, $f_{\theta} =0$, and spin parameter $a=0.999m$.
• Figure 5: WH1 spacetime with plasma distribution $f_\theta = \omega{_c}{^2}m{^2}(1+2\sin{^2}\theta)$, $f_r =0$, and spin parameter $a=0.999m$.