Photon rings and shadows of Kerr black holes immersed in a swirling universe

TL;DR

KBHSU studies photon rings and shadows around a Kerr black hole embedded in a swirling universe produced by an Ehlers transformation within the Ernst formalism. The spin–swirl coupling breaks equatorial symmetry and can yield up to three light rings at the critical value $ajM=0.25$, with radii typically distinct. Because the spacetime is not separable, light rings are located from stationary points of $H_\pm$ with $H_\pm = \omega \pm F\rho$, and shadows are computed through backward ray-tracing, revealing twisted, asymmetric silhouettes that depart from the pure Kerr and Schwarzschild cases. The analysis also characterizes conical deficits and ergoregion topology, highlighting a transition near $ajM=0.25$ and suggesting potential connections to rotating cosmic structures and chaotic geodesic dynamics as avenues for future work.

Abstract

We discuss photon rings around as well as shadows of Kerr black holes immersed in a swirling spacetime. We find that the spin-spin interaction between the angular momentum of the black hole and the swirling of the background leads to new interesting effects as it breaks the symmetry between the upper and lower hemispheres. One of the new features of the spin-spin interaction is the existence of up to three light rings for suitable choices of the angular momentum parameter $a$ and swirling parameter $j$. In comparison to the Schwarzschild black hole immersed in a swirling universe, the light rings typically all possess different radii.

Figures (7)

• Figure 1: Cross section ($x=r \sin\theta \cos\varphi$, $y = r \sin\theta \sin\varphi$, $z=r\cos\theta$, with $\varphi=0,\pi$) of the ergoregions (coloured) with different values of $jM^2$ and (a) $a=0.1M$ and (b) $a=0.8M$. The angular velocity of frame dragging $\Omega=\omega$ in these regions is positive when coloured blue and negative when coloured red. The region behind the event horizon $r<r_h^{(+)}$ has been excluded from these plots.
• Figure 2: Locations of LRs at multiples of $jM^2=0.002$ with $M=1$. In the left-hand column we plot the coordinates of the LRs in the $(r, \theta)$-plane, in the middle column we give the radial coordinate against $j$, and in the right-hand column we show the polar coordinate against $j$. LRs corresponding to $H_+$ are coloured blue, and LRs corresponding to $H_-$ are in orange. The thick black dashed line represents the radius of the outer horizon. The pink vertical strip highlights the region where three LRs occur for the same value of $j$. The third LR appears around $ajM=0.25$ and always begins at the North pole $\theta=0$. The colours of the curves indicate whether the LR is a root of $H_+$ (light blue) or $H_-$ (orange).
• Figure 3: Location of photon rings in the $(r,\theta)$-plane for $a=0.5M$ (upper row) and $a=0.9M$ (lower row). The ergoregions are highlighted in light blue and the vertical dashed line represents the radius of the event horizon. The direction of rotation of the light rings is indicated by their colour : prograde orbits are represented by blue dots, while retrograde ones are represented by red dots. Note that prograde and retrograde here are with respect to the direction of the black hole rotation.
• Figure 4: (a) A schematic representation of the numerical setup. The small black sphere represents the observer, while the sphere with four coloured sections represents the celestial sphere (or the observer's sky). The observer's field of view is represented by a pentahedron in dark gray, resulting in the image seen by the observer. In (b), we show the view from a Minkowski spacetime, while in (c), the view is from a swirling universe with j = 0.0005.
• Figure 5: We show the lensing images for a rapidly rotating KBHSU with $a = 0.9M$ and different values of the swirling parameter $j$. The observer is set on the equatorial plane at $r_o = 15$.