Shadows cast by a class of rotating black bounces with an anisotropic fluid

TL;DR

Working in signature $(-,+,+,+)$ and units with $c=G=1$, the paper studies shadows cast by rotating black bounces sourced by an anisotropic fluid. It constructs rotating solutions via a generalized Newman–Janis/Azreg‑Aïnou method, derives separable photon geodesics, and obtains shadow boundaries for arbitrary inclination, validating analytic contours with PyHole backward ray tracing. Depending on parameters, shadows range from Kerr-like to highly deformed, including horizonless, throat-dominated silhouettes where the wormhole throat can imprint the boundary through a turning-point mechanism rather than a photon sphere. This yields novel shadow signatures that could help distinguish black bounce/wormhole spacetimes from standard Kerr black holes in high-resolution shadow observations.

Abstract

In this work, we introduce a family of rotating black bounces with an anisotropic fluid obtained by using a modified Newman-Janis algorithm. We analyze the main features of these spacetimes and obtain the geodesics for photons, which admit the separation of the Hamilton-Jacobi equation. We then determine the shape of the shadow in terms of the parameters of the model. We present some relevant examples that exhibit some traits that distinguish these spacetimes from other related ones appearing in the literature.

Figures (7)

• Figure 1: Plot of the function $\mathcal{F}$ with $m=1$: (\ref{['f_omega_1']}) $\omega=1$ and (\ref{['f_omega_1_4']}) $\omega=1/4$.
• Figure 2: Plots of $\Delta(r)$ for the different cases, all of them with $\omega=m=1$ and $\rho_0=0.2$. (\ref{['case1']}) $l=0.05$ (case 1). (\ref{['case2']}) $\mathcal{F}(l\simeq0.106,\omega,m)=\rho_0$ (case 2). (\ref{['case3']}) $l=0.15$ (case 3). (\ref{['case4']}) $l=0.5$ (case 4). (\ref{['case5']}) $\mathcal{F}(l\simeq1.894,\omega,m)=\rho_0$ (case 5). (\ref{['case6']}) $l=2$ (case 6). Note that $\omega=m=1$ leads to $\mathcal{F}_{max}=1$, with $l_{max}=1$.
• Figure 3: Regions with different horizon structures in the parameter space $(a,l)$ for different cases, all of them with $m=1$. (\ref{['omega_1_4']}) $\omega=1/4$, $\rho_0=0.5$. (\ref{['rho02']}) $\omega=1$, $\rho_0=0.2$. (\ref{['rho09']}) $\omega=1$, $\rho_0=0.9$. (\ref{['rho12']}) $\omega=1$, $\rho_0=1.2$. The black lines indicate the cases where $\rho_0=\mathcal{F}(l,\omega,m)$.
• Figure 4: Different possibilities for the plots of $V_{eff}$ in the cases 1 without horizons and 6. In all plots $\omega=m=1$, $\rho_0=0.9$, $l=1.5$, and $\eta=0$. (\ref{['pot1']}) $a=2$ and $\xi=-7.8$; we start with a maximum with a positive value and $\lim\limits_{r\to 0}V_{eff}=+\infty$, the turning point is given by the highest root. (\ref{['pot2']}) $a=2$ and $\xi=-7.3$; now the maximum is negative but we still have $\lim\limits_{r\to 0}V_{eff}=+\infty$, so we still have a return (no shadow yet). (\ref{['pot4']}) $a=0.2$ and $\xi=-5.5$; the other possibility is that we have a positive maximum but $\lim\limits_{r\to 0}V_{eff}=-\infty$, so $r=0$ has no contribution to the shadow boundary. (\ref{['pot3']}) $a=2$ and $\xi=-3.8$; finally we have $\lim\limits_{r\to 0}V_{eff}=-\infty$ and a negative maximum, so this light ray is inside the shadow.
• Figure 5: Examples of shadows arising in cases 1 without horizons and 6, produced by the two possible mechanisms: the photon sphere (outside the throat) and the wormhole throat. All plots correspond to $\omega=m=1$. The rows show different observer inclination angles: $\theta_0=\pi/2$ (top), $\theta_0=\pi/6$ (middle), and $\theta_0=0$ (bottom). The three columns correspond to different parameter choices: $\rho_0=0.9$, $l=1.5$, $a=2$ (left); $\rho_0=0.9$, $l=1.5$, $a=0.2$ (center); $\rho_0=1.05$, $l=0.5$, $a=0$ (right). See text for a detailed discussion.