Fuzzballs are believed by string theorists to be the true quantum description of black holes. Put forward by Samir Mathur of Ohio State University in 2002, fuzzballs are giant, compact star like objects comprised entirely of intertwined strings. String theory is a theory of quantum gravity, for a recap see How long is a piece of string. These seemingly cuddly and cute entities are actually proposed to be very powerful indeed and in their suggested reformulation of black holes, are supposedly able to resolve some of the biggest problems within theoretical physics.

To understand fuzzballs we must first remind ourselves of the key properties of black holes. Earlier posts in the Black Holes series (#1, #2, #3, #4) at RTU cover these fantastical features in more depth, but in a nutshell they are defined by two key features. Firstly, the event horizon, the barrier from which information cannot escape. Secondly, the singularity, the point at the very centre of the black hole at which, due to an infinity matter density, space and time as we know them breakdown. The problem with the original black hole view is that the nature of these beasts can be described through both the quantum lens and the gravity lens. The two leading theories of the universe have been unable to reconcile their differences and their clash, in the context of black holes, has caused arguably the most troublesome conflict in the subject, the information paradox. This, coupled with the seemingly impossible understanding of a singularity has caused physicists to tear their hair out over the years. Fuzzballs, claim to present solutions to both these problems. To understand these let us take each problem and its supposed resolution in turn.

**The information paradox**

*The Black Hole*

In the standard description of a black hole there exists the infamous event horizon – a boundary a distance from the centre of the black hole from which nothing can escape. A point of no return. Hawking realised that in the empty space surrounding this horizon there can enter into existence, particle and anti-particle pairs. If this happens, there is chance that one of these pairs will escape outwards, while the other passes through the event horizon of the black hole, never to be seen again. As a result of the outwardly escaping particle, the black hole is seen to be radiating and with a loss of energy through radiation comes a shrinking of the black hole. For a dedicated explanation of this process see Black Holes: #2 Glowing and Shrinking. As a result of this ongoing phenomena, a black hole will finally cease to exist altogether, having evaporated entirely. In doing so, information of whatever fell into the black hole will be destroyed and this destruction of information is staunchly in opposition to the laws of quantum mechanics. In quantum mechanics, information is *never* lost. General Relativity also states that a black hole is characterised only by its mass, spin and charge. There is no other information that can be deduced about a black hole from examination of its event horizon. This lack of information and eventual disappearance of it altogether is known as *the information paradox.*

*The Fuzzball *

The fuzzball view claims to resolve this paradox with doing away with the event horizon altogether. The theory instead claims that these extremely dense coagulations of matter are comprised entirely of strings and *do* have a physical surface, just like a neutron star, ordinary star, or planet does. This surface however, is fuzzy instead of entirely solid. The diagram below may help your visualisation.

By eliminating the event horizon, we eliminate the phenomena of Hawking radiation as information can not longer be lost past a boundary or no return as there *is *no boundary of no return. Radiation still gets emitted from the fuzzball if one particle falls in and the other escapes but there is no clash with quantum mechanics. The information about the infalling particle can be retrieved. Furthermore because the fuzzball has a surface, there is structure here and information about the past history of the fuzzball can be deduced from it. From analysis of this structure all fuzzballs are seen to be unique and are characterised by a lot more than just their mass, spin and charge. As John Wheeler famously said to sum up the generic nature of black holes, ‘a black has no hair’. Fuzzballs however very much do have hair, and knotty hair at that.

**The singularity**

*The Black Hole*

Another troubling feature of the black hole is the point at the very centre where space and time breakdown due to the extreme density of matter. In the standard theory of general relativity the curvature of spacetime tends towards infinity with the mathematics blowing up in our faces, producing seemingly unphysical results.

*The Fuzzball*

The fuzzball structure, as we have said, is made from strings – as, according to string theory, is everything in our universe as they are the fundamental components of matter. As objects fall into the fuzzball, their strings combine with those on fuzzball’s surface forming larger, more complex string structures. When these strings combine together there is resultant outward pressure from the massless fields at play. At the centre of the fuzzball the density of these strings is at its highest and the strong resultant outward pressure causes a phase transition to a new state of matter which prevents the formation of a singularity. Perhaps a little hard to swallow without examining the maths first hand but i’m giving you the quick and dirty jist of it.

*a) the black hole view with singularity in spacetime represented by a jagged line*

*b) the fuzzball view with the centre of the fuzzball represented by a dense coagulation of strings*

**Entropy**

Another advocate for fuzzballs is entropy. As required by the second law of thermodynamics, black holes have entropy – an inherent measure of their level of disorder or simply put, chaos. All systems have a measure of entropy and this entropy can be quantified by counting the number of microstates of the system. Different microstates are the different ways the components of the system can be arranged whilst preserving the overall macroscopic picture. For example a messy room has a high entropy as the items can be strewn around in many ways, i.e. a large number of microstates, whilst still preserving the overall look of messiness.

In 1973 Bekenstein postulated that the level of this entropy associated to the black hole is proportional area of the black hole’s event horizon. Together with Hawking, the formula for a black hole’s entropy was produced, expressing it as proportional to the area of the horizon with factors of fundamental constants. It is a truly remarkable formula as it includes the fundamental constant of gravity and a fundamental constant of the quantum world, the planck length. Such constants rarely meet in our descriptions of nature, given the long standing incompatibility of quantum mechanics and general relativity. In the original black hole view, the only way we can measure this entropy is from properties of the event horizon since we cannot retrieve any further information from inside.

The fuzzball theory however, allows us to directly count the number of microstates of the system. Within string theory, a black hole’s structure comes in the forms of strings and branes and the ways in which these can be arranged represent the different microstates. Mathur’s calculation of the entropy from analysing these microstates can be found to equal that found by the Bekenstein-Hawking formula! A very promising find.

**Fuzzy thoughts**

Fuzzballs present a way to reconcile classical and quantum descriptions of black holes, however the jury is still out in the theoretical physics community. Fuzzballs make use of string theory, much to the delight of many who have poured over its formulation as a possible quantum gravity theory. However, string theory is by no means a complete theory and the fuzzballs rely heavily on its claims. Although the framework seemingly resolves problems of singularities and information destruction, it raises new questions in lieu, including the nature of extra dimensions to name one (did I mention, string theory is at minimum 10 dimensional?!) And… as much as the event horizon of a black hole is a wicked feature, physicists have a somewhat twisted affinity for it. Not all are keen to champion its dismissal and instead would rather find a theory which resolves the paradox whilst maintaining its inclusion.

The final fate of the fuzz is still unknown.

Long live the fuzz!

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