Twisting shadows: light rings, lensing and shadows of black holes in swirling universes

Twisting shadows: light rings, lensing and shadows of black holes in swirling universes

11 Jan 2024 | Zeus S. Moreira, Carlos A. R. Herdeiro, Luís C. B. Crispino
This paper investigates the behavior of light in a vacuum solution of the Einstein field equations describing a Schwarzschild black hole (BH) immersed in a rotating background, known as a swirling universe (SU). The SU is characterized by the peculiar property that the north and south hemispheres spin in opposite directions, and it does not contain closed timelike curves. Using the Ernst formalism, the authors construct a solution for the SU and analyze the null geodesic flow, focusing on the existence of light rings (LRs). They find that there is one unstable LR for each rotation sense of the background. The SU drives the Schwarzschild BH LRs outside the equatorial plane, displaying counter-rotating motion with respect to each other, while both co-rotating with respect to the SU. Using backward ray-tracing, they obtain the shadow and gravitational lensing effects, revealing a novel feature for observers on the equatorial plane: the BH shadow displays an odd $ Z_2 $ (north-south) symmetry, inherited from the SU's symmetry. The paper also discusses the topological charge of the SU, showing that there is one unstable LR for each potential, and that the SU has no LRs. The study of the shadow and gravitational lensing of the SBHSU solution reveals that the shadow is $ Z_2 $-odd, indicating a north-south symmetry, and that the SU has no LRs. The paper concludes that the LR of the SBHSU spacetime is actually the LR inherited from the Schwarzschild BH that was split and pushed off the equator by the swirling background.This paper investigates the behavior of light in a vacuum solution of the Einstein field equations describing a Schwarzschild black hole (BH) immersed in a rotating background, known as a swirling universe (SU). The SU is characterized by the peculiar property that the north and south hemispheres spin in opposite directions, and it does not contain closed timelike curves. Using the Ernst formalism, the authors construct a solution for the SU and analyze the null geodesic flow, focusing on the existence of light rings (LRs). They find that there is one unstable LR for each rotation sense of the background. The SU drives the Schwarzschild BH LRs outside the equatorial plane, displaying counter-rotating motion with respect to each other, while both co-rotating with respect to the SU. Using backward ray-tracing, they obtain the shadow and gravitational lensing effects, revealing a novel feature for observers on the equatorial plane: the BH shadow displays an odd $ Z_2 $ (north-south) symmetry, inherited from the SU's symmetry. The paper also discusses the topological charge of the SU, showing that there is one unstable LR for each potential, and that the SU has no LRs. The study of the shadow and gravitational lensing of the SBHSU solution reveals that the shadow is $ Z_2 $-odd, indicating a north-south symmetry, and that the SU has no LRs. The paper concludes that the LR of the SBHSU spacetime is actually the LR inherited from the Schwarzschild BH that was split and pushed off the equator by the swirling background.
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Understanding Twisting shadows%3A Light rings%2C lensing%2C and shadows of black holes in swirling universes