[Apr. 18, 2023: JD Shavit, The Brighter Side of News]

###### A disc of glowing gas swirls in the “Gargantua” black hole from the movie Interstellar. Because space curves around the black hole, it is possible to look out the other side and see the part of the disk of gas that would otherwise be hidden by the hole. Our understanding of this mechanism has now been enhanced by Albert Sneppen, a Danish master’s student at the NBI (CREDIT: interstellar.wiki/CC BY-NC License).

Black holes have always fascinated scientists and the general public. These phenomena are so mysterious that even light cannot escape their gravitational pull. Space and time around black holes behave oddly, making the curvature of space so intense that light rays are deflected.

This deviation has a unique property; very close light can be deflected so much that it travels through the black hole several times. Therefore, when we observe a distant background galaxy or any other celestial body, we might be lucky enough to see multiple versions of the same object.

This phenomenon, known as gravitational lensing, has been known for decades, but it was only recently that a new, more precise mathematical expression was discovered.

This mathematical expression, developed by Albert Sneppen, a student at the Niels Bohr Institute, sheds light on this particular phenomenon and has just been published in the journal journal Scientific Reports.

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The mechanism of gravitational lensing is shown in the figure below. A distant galaxy shines in all directions, and some of its light approaches the black hole and is deflected slightly. A light comes even closer, goes around the hole once before escaping to us, and so on. As we get closer to the black hole, we see more and more versions of the same galaxy the closer we get to the edge of the hole.

###### Light from the background galaxy orbits a black hole an increasing number of times the closer it passes to the hole, and so we see the same galaxy in more than one direction (credit: Peter Laursen).

## mathematical expression

The mathematical expression that describes the phenomenon of gravitational lensing has been known for more than 40 years. It’s a factor of 500, which means that to see the next image, you have to look 500 times closer to the black hole than the previous image. This factor is complicated to calculate, and until recently there was no mathematical and physical intuition as to why it was this exact factor.

###### The situation seen “from the front”, that is to say how it would actually be observed from Earth. Additional images of the galaxy become increasingly compressed and distorted the closer we look at the black hole (CREDIT: Peter Laursen)

Albert Sneppen, using some nifty mathematical tricks, has now succeeded in proving why this factor is true. “There is something incredibly beautiful about understanding now why images repeat so elegantly. On top of that, it offers new opportunities to test our understanding of gravity and black holes,” says Albert Sneppen.

This mathematical proof is not only satisfying in itself, but it also brings us closer to understanding this wonderful phenomenon. The 500 factor stems directly from how black holes and gravity work, so image repeats now become a way to examine and test gravity.

###### Simulated rays of light satisfying Eq. (3) with δ0<0 (à gauche) et δ0>0 (right) with coloring indicating the magnitude of δ0. The black hole is shaded in gray with the orbit of the last photon indicated by a dashed gray line. Each successive light path traced is a factor of 2 closer to the photon capture radius with the resulting deflection angle increasing just below 40∘. Thus, the logarithmic scaling to the photon capture radius corresponds to a linear evolution of ϕ. (CREDIT: Scientific Reports)

## Rotating black holes

Sneppen’s mathematical method can also be generalized to apply not only to “trival” black holes but also to rotating black holes. In fact, all black holes rotate. When the black hole is spinning very fast, we no longer have to get closer to the black hole by a factor of 500, but significantly less. Each frame is now only 50.5 or even up to two times closer to the edge of the black hole.

Having to look 500 times closer to the black hole for each new image means the images are quickly “squeezed” into a single ring image, as shown in the figure to the right. In practice, the many images will be difficult to observe.

###### Full (left) and enlarged (right) phase space portrait for light trajectories obeying eq. (3) with the coloring of the arrows indicating the magnitude of the change (lighter shades imply longer vectors). (CREDIT: Scientific Reports)

But when black holes spin, there’s more room for “extra” images, so we can hope to confirm the theory through observation in the near future. This way, we can learn not only about black holes, but also about the galaxies behind them.

The travel time of light increases with the number of times it has to go around the black hole, so the images become more and more “delayed”. If, for example, a star explodes as a supernova in a background galaxy, one might see that explosion over and over again.

The implications of Sneppen’s research are vast, and he’s sure to inspire a new generation of scientists to explore the mysteries of the universe using the powerful tool of gravitational lensing.

*For more science stories, check out our New Discoveries section at **The bright side of the news**.*

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