# String Theory’s Fuzzy Balls Solve the Famous Black Hole Paradox

*Scientists have turned to string theory to better understand black holes, proposing that they can be modeled as “fuzzy balls” made up of interacting strings.*

Black holes are among the most mysterious objects in the universe. For more than a century, physicists have used Einstein’s theory of general relativity to describe them, treating gravity as a distortion of spacetime created by the energy and momentum of particles and fields. .

In this theory, a black hole is considered to be an infinitely dense point called a singularity, which is surrounded by a spherical surface known as the event horizon – or simply a horizon for short – with empty space existing between them. The gravity in the region below the horizon is so strong that no particle or wave can escape it and is doomed to fall into the singularity.

In this theory, black holes are characterized by only three parameters: mass, electric charge and angular momentum encoding its rotational properties. However, this contradicts a principle of quantum mechanics called a time evolution unit, which states that information should not be lost during the temporal development of a physical system.

Black holes are formed from massive amounts of matter made up of huge numbers of particles that each have their own set of physical parameters. If the classic description of black holes is correct, then the “information” about the matter used to create them has definitely been lost given the simplicity of that description implied by the “no hair” theorem. This is called the black hole information loss paradox.

A group of American physicists led by Samir Mathur of Ohio State University sought to resolve the paradox in a new paper published in the *Turkish Journal of Physics*. They propose replacing the convenient general relativistic image of black holes as empty space with all its mass located at its center, with a ball-like mess of interacting strings called “fuzzy balls”.

These hypothetical objects have no horizon or singularity, and sizes similar to black holes of the same mass. This black hole fuzzy ball concept is based on string theory, a modern theory whose central postulate is that elementary particles, often thought of as point-like, are actually tiny vibrating strings with different modes of oscillation that correspond to different types of particles. These fuzzy balls of string theory are not characterized by three numbers, but by a large number of parameters composed of all the strings that compose them, solving the paradox of the loss of information.

Black hole fuzzy balls also help rectify another paradox of black hole physics. In the 1970s, Stephen Hawking analyzed the electromagnetic field in the vicinity of a horizon and predicted that black holes emit photons in the same way as heated bodies, such as stars or burning pieces of coal.

The mechanism of this hypothetical radiation emitted by a black hole results from the creation of photons in the vacuum outside its horizon due to quantum effects. Some of these particles cross the horizon and fall on the singularity, while others manage to escape the black hole’s gravitational field and move away. In principle, they can be observed in the same way as we see the light emitted by the Sun and other hot bodies. This radiation is known as Hawking radiation and has not yet been detected because its energy is so low that it exceeds the sensitivity of current instruments.

The difference between the Hawking radiation of black holes and the emissions of electromagnetic waves from heated bodies such as stars, for example, is that in the latter, the photons are generated by elementary particles in interaction, and not in a vacuum.

Because of this peculiarity in the way black hole radiation is generated, photons emitted during a black hole’s lifetime would have too great an entropy for the process to be consistent with general principles of quantum mechanics, which require that this entropy be less than the entropy of the black hole.

In order to resolve this paradox, physicists considered something called a “wormhole paradigmwhich requires that photons that escape the black hole’s gravitational field as well as particles that fall into it be taken into account when considering entropy. If one defines Hawking radiation as a union of these two sets of particles, then the quantum mechanical correlations between them reduce the entropy of the black hole radiation, resolving the paradox.

But the Ohio State researchers’ analysis suggests that all realizations of this paradigm either lead to higher non-physical probabilities of one of certain phenomena – the aforementioned violation of unitarity – or to a violation of the original proposal of Hawking that black holes radiate like heated bodies. Instead, Mathur and his colleagues found that these problems do not arise if black holes are viewed not as objects with a singularity and a horizon, but as fuzzy balls of string theory with radiation produced. by the interacting strings.

While the theory may work on paper, detecting this low-energy radiation is another challenge. It was predicted that the interaction between the black hole’s gravitational waves and the surface of the fuzzy ball would leave an imprint in its spectrum. Many scientists hope to be able to record such a subtle change with the next generation of terrestrial and space gravitational observatories, allowing them to determine whether hairballs are real or not.

*Reference: Bin Guo, et al., **Comparing fuzzy ball and wormhole paradigms for black holes**Turkish Journal of Physics (2021), arXiv:2111.05295*

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