# Mathematicians have figured out what the reflection of the universe looks like in the light around a black hole

(ORDO NEWS) — Astronomers have developed equations to accurately describe the reflections of the universe that form in distorted light around a black hole.

The proximity of each reflection depends on the viewing angle relative to the black hole and the speed of rotation of the black hole.

This came to light thanks to a mathematical approach developed in July 2021 by physics student Albert Sneppen from the Niels Bohr Institute in Denmark.

This gave astronomers a new tool to study the gravitational environment around these extreme objects.

“There is something fantastically beautiful about now understanding why the images are repeated in such an elegant way,” Snappen said.

“In addition, it provides new opportunities to test our understanding of gravity and black holes.”

If there is one thing that black holes are famous for, it is their extreme gravity. For example, beyond a certain radius, the speed of light in a vacuum is insufficient to achieve the escape velocity.

This point of no return is called the event horizon, which is defined by the so-called Schwarzschild radius, and it is for this reason that we say that even light cannot escape the black hole’s gravity.

However, beyond the event horizon of a black hole, the environment is also seriously disturbed. The gravitational field is so powerful that the curvature of space-time is nearly circular.

Any photons entering this space must naturally follow this curvature. This means that, from our point of view, the path of light appears to be distorted and curved.

At the very inner edge of this space, just beyond the event horizon, we can see what is called the photon ring, where photons orbit the black hole several times before either falling into the black hole or escaping into space .

This means that light from distant objects behind a black hole can be magnified, distorted, and “reflected” multiple times. Astronomers call this the gravitational lens. This effect is a useful tool for studying the universe.

So we’ve known about the effect for some time, and scientists have figured out that the closer you look into a black hole, the more reflections you see from distant objects.

To go from one image to the next image, you had to look about 500 times closer to the optical edge of a black hole or an exponential function of two pi (e2π), but why this was so was difficult to describe mathematically.

Sneppen’s approach was to reformulate the trajectory of light and quantify its linear stability using second-order differential equations.

He found that his solution not only mathematically describes why images repeat at e2π distances, but that it can work for a rotating black hole and that the repetition distance depends on rotation.

“It turns out that when it spins really fast, you no longer have to get 500 times closer to the black hole, but much less,” Snappen said.

“In fact, each image is now only 50, or five, or even just two times closer to the edge of the black hole.”

In practice, this will be hard to see, at least not anytime soon – just look at the intense amount of work that has gone into unresolved imaging of the ring of light around the supermassive black hole Povekha (M87*).

However, theoretically, there should be an infinite number of rings of light around a black hole.

Since we once imaged the shadow of a supermassive black hole, we hope it’s only a matter of time before we can get better images, and there are already plans to image the photon ring.

One day, infinite images near a black hole may become a tool for studying not only the physics of black holes, but also the objects behind them – repeated in endless reflections at orbital infinity.

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