# What Are Black Holes in String Theory?

*Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.*

String theory is a dense and not easily accessible field. Trying to understand it takes time and patience, and to explain it to others involves even more. String theory has so much math and uncommon aspects to it that trying to explain it is a tricky and oftentimes frustrating task. So with that in mind, I hope you enjoy this article and are able to learn from it. If you have any questions or feel I need to do more, please leave me a comment at the end and I will get to fixing it. Thanks!

## Background

The main drive behind understanding black holes with string theory arose from research in the late 60s and early 70s. Work led by Demetrios Christodoulou, Werner Israel, Richard Price, Brandon Carter, Roy Ken, David Robinson, Stephen Hawking, and Roger Penrose examined how black holes operate with quantum mechanics, and many interesting findings such as the no-hair theorem were found. Simply put, it states that no matter the initial conditions of what formed the singularity, any black hole can be described by its mass, spin, and electrical charge. And that’s it, no other features are present in a black hole. They *cause* other things to happen but those three are the quantities we can measure of them. Interestingly enough, elementary particles seem to have a similar situation, with some basic features describing them and nothing else (Greene 320-1).

This got people wondering what would happen if a black hole was small, say like an elementary particle. Relativity places no restrictions on the mass of a black hole, so long as the gravity required to condense it exists. So…does a smaller and smaller black hole begin to look like an elementary particle? To figure that out, we need quantum mechanics which does not work well on a macroscopic scale like say with the black holes we are familiar with. But we are not dealing with that if we keep shrinking down to the Planck scale. We need something that will help merge quantum mechanics and relativity if we want to figure this out. String theory is a possible solution (321-2).

## Getting Familiar with Dimensional Space

This is where the mathematics of science began to take a giant leap. In the late 1980s, physicists and mathematicians realized that when 6-dimensions (yeah, I know: who thinks about that?) are folded into a Calabi-Yau space (a geometrical construct), then two types of spheres will be inside that shape: a 2-dimensional sphere (which is just surface of an object) and a 3-dimentional sphere (which is surface of an object spread *everywhere*). I know, this is already tough to grasp. You see, in string theory they start out with a 0-dimension, aka the string, and other dimensions depend on the *type* of object we are referring to. In this discussion, we are referring to spheres as our base shape. Helpful? (322)

As time progresses, the volume of those 3-D spheres in the Calabi-Yau space becomes smaller and smaller. What happens to space-time, our 4-D, as those spheres collapse? Well, strings can catch 2-D spheres (because a 2-D world can have a 2-D sphere for a surface). But our 3-D world has an extra dimension (called time) that cannot be surrounded by moving string and thus we lose that protection and so the theory predicts our Universe should stop because now we would be dealing with infinite quantities that are not possible (323).

## Branes

Enter Andrew Strominger, who in 1995 switched the focus of String theory at that point, which was on 1-D strings, to instead on branes. These can surround spaces, like a 1-D brane around a 1-D space. He was able to find that the trend did hold for 3-D as well and using “simple” physics was able to show that 3-D branes prevent a runaway effect for the Universe (324).

Brian Greene realized that the answer wasn’t as simple as that, however. He found that a 2-D sphere, when it gets squeezed to a miniscule point, rips occur in its structure. However, the sphere will restructure itself to seal the rip. Now, what about 3-D spheres? Greene along with Dave Morrison built on the work from the late 80s Herb Clemens, Robert Friedman, and Miles Reid to show that the 3-D equivalent would be true, with one little caveat: the repaired sphere is now 2-D! (think like a broken balloon) The shape is now completely different, and the location of the tear causes one Calibri-Yau shape to become another (325, 327).

## Back to Our Feature

Okay, that was a lot of information that seemed unrelated to our initial discussion. Let us pull back and regroup here. A black hole, for us, is a 3-D space, but String Theory refers to them as a “unwrapped brane configuration.” When you look at the mathematics behind the work, it does point to that conclusion. Strominger’s work also showed that the mass of the 3-D brane we call a black hole would be directly proportional to its volume. And as mass approaches zero so will the volume. Not only would the shape change but the string pattern would also. The Calabi-Yau space undergoes a phase change from one space to another. Thus, as a black hole shrinks down, String Theory predicts that the object will indeed change – into a photon! (329-32)

But it gets better. The event horizon of a black hole is considered by many to be the final boundary between the Universe we are used to and that which is forever departed from us. But rather than treating the event horizon as the gateway to the interior of a black hole, String Theory predicts that it is instead the destination of the information that encounters a black hole. It creates a hologram that is forever imprinted in the universe on the brane surrounding the black hole, where all those loose strings begin to fall under primordial conditions and act like they did at the beginning of the Universe. In this view, a black hole is a solid object and therefore has nothing beyond the event horizon (Seidel).

## Works Cited

Greene, Brian. The Elegant Universe. Vintage Books, New York, 2^{nd}. Ed., 2003. Print. 320-5, 327, 329-37.

Seidel, Jamie. “String theory takes the hole out of black holes.” *News.com.au.* News Limited, 22 June 2016. Web. 26 Sept. 2017.

**© 2017 Leonard Kelley**

## Comments

**Leonard Kelley (author)** on November 19, 2018:

Thank you for those kind words, dane. I'm glad you enjoyed the article!