In the vicinity of black holes, space is so warped that even light rays may
curve around them several times. This phenomenon may enable us to see multiple
versions of the same thing. While this has been known for decades, only now do
we have an exact, mathematical expression, thanks to Albert Sneppen, student
at the Niels Bohr Institute. The result, which even is more useful in
realistic black holes, has just been published in the journal Scientific
Reports.

You have probably heard of black holes -- the marvelous lumps of gravity
from which not even light can escape. You may also have heard that space
itself and even time behave oddly near black holes; space is warped.

In the vicinity of a black hole, space curves so much that light rays are
deflected, and very nearby light can be deflected so much that it travels
several times around the black hole. Hence, when we observe a distant
background galaxy (or some other celestial body), we may be lucky to see the
same image of the galaxy multiple times, albeit more and more distorted.

### Galaxies in multiple versions

The mechanism: A distant galaxy shines in all directions -- some of its
light comes close to the black hole and is lightly deflected; some light
comes even closer and circumvolves the hole a single time before escaping
down to us, and so on. Looking near the black hole, we see more and more
versions of the same galaxy, the closer to the edge of the hole we are
looking.

How much closer to the black hole do you have to look from one image to see
the next image? The result has been known for over 40 years, and is some 500
times (for the math aficionados, it is more accurately the "exponential
function of two pi," written e2π).

Calculating this is so complicated that, until recently, we had not yet
developed a mathematical and physical intuition as to why it happens to be
this exact factor. But using some clever, mathematical tricks, master's
student Albert Sneppen from the Cosmic Dawn Center -- a basic research
center under both the Niels Bohr Institute and DTU Space -- has now
succeeded in proving why.

"There is something fantastically beautiful in now understanding why the
images repeat themselves in such an elegant way. On top of that, it provides
new opportunities to test our understanding of gravity and black holes,"
Albert Sneppen clarifies.

Proving something mathematically is not only satisfying in itself; indeed,
it brings us closer to an understanding of this marvelous phenomenon. The
factor "500" follows directly from how black holes and gravity work, so the
repetitions of the images now become a way to examine and test gravity.

### Spinning black holes

As a completely new feature, Sneppen's method can also be generalized to
apply not only to "trivial" black holes, but also to black holes that
rotate. Which, in fact, they all do.

"It turns out that when the it rotates really fast, you no longer have to
get closer to the black hole by a factor 500, but significantly less. In
fact, each image is now only 50, or 5, or even down to just 2 times closer
to the edge of the black hole," explains Albert Sneppen.

Having to look 500 times closer to the black hole for each new image, means
that the images are quickly "squeezed" into one annular image. In practice,
the many images will be difficult to observe. But when black holes rotate,
there is more room for the "extra" images, so we can hope to confirm the
theory observationally in a not-too-distant future. In this way, we can
learn about not just black holes, but also the galaxies behind them:

The travel time of the light increases, the more times it has to go around
the black hole, so the images become increasingly "delayed." If, for
example, a star explodes as a supernova in a background galaxy, one would be
able to see this explosion again and again.

## Reference:

Albert Snepppen. Divergent reflections around the photon sphere of a black
hole. Scientific Reports, 2021; 11 (1) DOI:
10.1038/s41598-021-93595-w

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