Using the Ernst formalism, a novel solution of vacuum General Relativity was

recently obtained [1], describing a Schwarzschild black hole (BH) immersed in a

non-asymptotically flat rotating background, dubbed swirling universe, with the

peculiar property that north and south hemispheres spin in opposite directions.

We investigate the null geodesic flow and, in particular, the existence of

light rings in this vacuum geometry. By evaluating the total topological charge

$w$, we show that there exists one unstable light ring ($w=-1$) for each

rotation sense of the background. We observe that the swirling background

drives the Schwarzschild BH light rings outside the equatorial plane,

displaying counter-rotating motion with respect to each other, while (both)

co-rotating with respect to the swirling universe. Using backwards ray-tracing,

we obtain the shadow and gravitational lensing effects, revealing a novel

feature for observers on the equatorial plane: the BH shadow displays an odd

$mathbb{Z}_2$ (north-south) symmetry, inherited from the same type of symmetry

of the spacetime itself: a twisted shadow.

Recent research has introduced a novel solution to vacuum General Relativity, using the Ernst formalism. This solution describes a Schwarzschild black hole surrounded by a non-asymptotically flat rotating background known as the swirling universe. What makes this swirling universe unique is that the north and south hemispheres rotate in opposite directions.

An investigation into the null geodesic flow in this vacuum geometry reveals the existence of light rings. By evaluating the total topological charge, it is determined that there is one unstable light ring for each rotation sense of the background. It is worth noting that light rings are points where photons can orbit around a black hole due to gravitational lensing.

The swirling background has an interesting effect on the Schwarzschild black hole’s light rings. It pushes them outside the equatorial plane, causing them to move in a counter-rotating motion with respect to each other while still co-rotating with the swirling universe. This means that the motion of the light rings is influenced by both the black hole and the background rotation.

Further investigation involves studying the shadow and gravitational lensing effects using backwards ray-tracing. The results reveal a unique feature for observers on the equatorial plane. The black hole shadow displays an odd $mathbb{Z}_2$ (north-south) symmetry, which is inherited from the twisted symmetry of the spacetime itself. This observation highlights a twisted shadow phenomenon attributed to the swirling universe.

## Future Roadmap:

- Continue studying the vacuum General Relativity solution obtained from the Ernst formalism.
- Explore the implications and consequences of a Schwarzschild black hole immersed in a swirling universe.
- Investigate how the twisting motion of the background affects other properties of the black hole, such as its event horizon.
- Further analyze the null geodesic flow and the behavior of light rings in this unique vacuum geometry.
- Investigate the impact of the swirling background on other astronomical phenomena like accretion disks and jets.
- Develop new techniques for studying the shadow and gravitational lensing effects of black holes in non-asymptotically flat backgrounds.
- Collaborate with observational astronomers to validate and test the predictions made by the twisted shadow phenomenon.
- Explore potential applications of the swirling universe concept in other branches of physics, such as quantum gravity.

## Potential Challenges:

- Obtaining precise and accurate measurements of light rings and their motion around the black hole in a swirling universe.
- Establishing a clear understanding of the mechanisms behind the twisting motion of the background and its effects on the black hole.
- Validating theoretical predictions through observations and finding suitable astronomical systems that exhibit similar characteristics.
- Overcoming technical obstacles in simulating and visualizing the shadow and gravitational lensing effects in non-asymptotically flat backgrounds.
- Navigating interdisciplinary collaborations to bridge theoretical studies with observational astronomy.

## Potential Opportunities:

- Advancing our understanding of general relativity and its behavior in unique astrophysical environments.
- Revealing new insights into the interaction between rotating backgrounds and black holes.
- Enhancing our ability to study and interpret observational data from black hole shadows and gravitational lensing.
- Expanding our knowledge of cosmic structures and their impact on various astrophysical phenomena.
- Opening doors for new research directions in theoretical physics, such as quantum gravity.