**Fuzzballs** are theorized by some

superstring theorySuperstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...

scientists to be the true

quantumQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

description of

black holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

s. The theory resolves two intractable problems that classic black holes pose for modern physics:

- The information paradox
The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...

wherein the quantum information bound in infalling matter and energy entirely disappears into a singularity; that is, the black hole would undergo zero physical change in its composition regardless of the nature of what fell into it.
- The singularity
A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

at the heart of the black hole, where conventional black hole theory says there is infinite spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

curvature due to an infinitely intense gravitational field from a region of zero volume. Modern physics breaks down when such parameters are infinite and zero.

Fuzzball theory replaces the singularity at the heart of a black hole by positing that the entire region within the black hole’s

event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

is actually a ball of

stringsA string is a hypothetical vibrating one-dimensional sub-atomic structure and one of the main objects of study in string theory, a branch of theoretical physics. There are different string theories, many of which are unified by M-theory. A string is an object with a one-dimensional spatial extent,...

, which are advanced as the ultimate building blocks of matter and energy. Strings are thought to be bundles of energy vibrating in complex ways in both the three physical dimensions of space as well as in

*compact directions*—extra dimensions interwoven in the

quantum foamQuantum foam, also referred to as spacetime foam, is a concept in quantum mechanics, devised by John Wheeler in 1955. The foam is supposed to be the foundations of the fabric of the universe. Additionally, it can be used as a qualitative description of subatomic spacetime turbulence at extremely...

(also known as

*spacetime foam)*.

## Physical characteristics

Samir Mathur of

Ohio State UniversityThe Ohio State University, commonly referred to as Ohio State, is a public research university located in Columbus, Ohio. It was originally founded in 1870 as a land-grant university and is currently the third largest university campus in the United States...

, with postdoctoral researcher Oleg Lunin, proposed via two papers in 2002 that black holes are actually spheres of strings with a definite volume; they are not a

singularityA gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

, which the classic view holds to be a zero-dimensional, zero-volume point into which a black hole’s entire mass is concentrated.

String theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

holds that the fundamental constituents of

subatomic particleIn physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...

s, including the

force carrierIn particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type...

s (e.g.,

quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...

s,

leptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...

s,

photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s, and

gluonGluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....

s), all comprise a one-dimensional string of energy that takes on its identity by vibrating in different modes and/or frequencies. Quite unlike the view of a black hole as a singularity, a small fuzzball can be thought of as an extra-dense

neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

where its neutrons have decomposed, or “melted,” liberating the quarks (strings in string theory) comprising them. Accordingly, fuzzballs can be regarded as the most extreme form of

degenerate matterDegenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...

.

Whereas the

event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

of a classic black hole is thought to be very well defined and distinct, Mathur and Lunin further calculated that the event horizon of a fuzzball would, at an extremely small scale (likely on the order of a few

Planck lengths), be very much like a mist: fuzzy, hence the name “fuzzball.” They also found that the physical surface of the fuzzball would have a radius equal to that of the event horizon of a classic black hole; for both, the

Schwarzschild radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...

for a median-size

stellar-mass black holeA stellar black hole is a black hole formed by the gravitational collapse of a massive star. They have masses ranging from about 3 to several tens of solar masses...

of 6.8

solar massThe solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...

es is 20 kilometers—roughly the size of the island of

KauaiKauai or Kauai, known as Tauai in the ancient Kaua'i dialect, is geologically the oldest of the main Hawaiian Islands. With an area of , it is the fourth largest of the main islands in the Hawaiian archipelago, and the 21st largest island in the United States. Known also as the "Garden Isle",...

in Hawaii.

With classical black holes, objects passing through the event horizon on their way to the singularity are thought to enter a realm of curved spacetime where the

escape velocityIn physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero gravitational potential energy is negative since gravity is an attractive force and the potential is defined to be zero at infinity...

exceeds the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. It is a realm that is devoid of all structure. Further, at the singularity—the heart of a classic black hole—spacetime is thought to have infinite curvature (that is, gravity is thought to have infinite intensity) since its mass is believed to have collapsed to zero (infinitely small) volume where it has infinite density. Such infinite conditions are problematic with known physics because key calculations utterly collapse. With a fuzzball, however, the strings comprising an object are believed to simply fall onto and absorb into the surface of the fuzzball, which corresponds to the event horizon—the threshold at which the escape velocity equals the speed of light.

A fuzzball

*is* a black hole; spacetime, photons, and all else that is not exquisitely close to the surface of a fuzzball are thought to be affected in precisely the same fashion as with a classic black hole featuring a singularity at its center. Classic black holes and fuzzballs differ only at the quantum level; that is, they differ only in their internal composition as well as how they affect

virtual particleIn physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...

s that form close to their event horizons (see

*Information paradox*, below). Fuzzball theory is thought by its proponents to be the true quantum description of black holes.

Since the volume of fuzzballs is a function of the Schwarzschild radius (2,954 meters per solar mass), fuzzballs have a variable density that decreases as the inverse square of their mass (twice the mass is twice the diameter, which is eight times the volume, resulting in one‑quarter the density). A typical 6.8solar-mass fuzzball would have a mean density of . A bit of such a fuzzball the size of a drop of water would have a mass of twenty million metric tons, which is the mass of a granite ball 240 meters in diameter. Though such densities are almost unimaginably extreme, they are, mathematically speaking, infinitely far from infinite density. Although the densities of typical stellar-mass fuzzballs are quite great—about the same as

neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

s—their densities are many orders of magnitude less than the

Planck density , which is equivalent to the mass of the universe packed into the volume of a single atomic nucleus.

Fuzzballs become less dense as their mass increases due to

*fractional tension.* When matter or energy (strings) fall onto a fuzzball, more strings aren’t simply added to the fuzzball; strings

*fuse together*, and in doing so, all the quantum information of the infalling strings becomes part of larger, more complex strings. Due to fractional tension, string tension exponentially decreases as they become more complex with more modes of vibration, relaxing to considerable lengths. The “mathematical beauty” of the string theory formulas Mathur and Lunin employed lies in how the fractional tension values produce fuzzball radii that precisely equal Schwarzschild radii, which

Karl SchwarzschildKarl Schwarzschild was a German physicist. He is also the father of astrophysicist Martin Schwarzschild.He is best known for providing the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished...

calculated using an entirely different mathematical technique 87 years earlier.

Due to the mass-density inverse-square rule, all fuzzballs need not have unimaginable densities. There are also

supermassive black holeA supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...

s, which are found at the center of virtually all galaxies. Sagittarius A*, the black hole at the center of our Milky Way galaxy, is 4.3 million solar masses. If it is actually a fuzzball, it has a mean density that is “only” 51 times that of gold. At 3.9 billion solar masses, near the upper bounds for supermassive black holes, a fuzzball would have a radius of 77

astronomical unitAn astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

s—about the same size as the termination shock of our solar system’s heliosphere—and a mean density equal to that of the Earth's atmosphere at sea level (1.2 kg/m

^{3}).

Irrespective of a fuzzball’s mass and resultant density, the determining factor establishing where its surface lies is the threshold at which the fuzzball’s escape velocity precisely equals the speed of light. Escape velocity, as its name suggests, is the velocity a body must achieve to escape from a massive object. For earth, this is 11.2 km/s. In the other direction, a massive object’s escape velocity is equal to the impact velocity achieved by a falling body that has fallen from the edge of a massive object’s sphere of gravitational influence. Thus, event horizons—for both classic black holes and fuzzballs—lie precisely at the point where spacetime has warped to such an extent that falling bodies just achieve the speed of light. According to

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

, via his

special theory of relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, the speed of light is the maximum permissible velocity in spacetime. At this velocity, infalling matter and energy impacts the surface of the fuzzball and its now-liberated, individual strings contribute to the fuzzball’s makeup.

## Information paradox

Classic black holes create a problem for physics known as the

black hole information paradoxThe black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...

, an issue first raised in 1972 by

Jacob BekensteinJacob David Bekenstein is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation.-Biography:...

and later popularized by

Stephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

. The information paradox is borne out of the realization that all the quantum nature (information) of the matter and energy that falls into a classic black hole is thought to entirely vanish from existence into the zero-volume singularity at its heart. For instance, a black hole that is feeding on the stellar atmosphere (protons, neutrons, and electrons) from a nearby companion star should, if it obeyed the known laws of quantum mechanics, technically grow to be increasingly different in composition from one that is feeding on light (photons) from neighboring stars. Yet, the implications of classic black hole theory are inescapable: other than the fact that the two classic black holes would become increasingly massive due to the infalling matter and energy, they would undergo zero change in their relative composition because their singularities

*have no composition.* Bekenstein noted that this theorized outcome violated the quantum mechanical law of

*reversibility*, which essentially holds that quantum information must not be lost in any process. This field of study is today known as

black hole thermodynamicsIn physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...

.

Even if quantum information was not extinguished in the singularity of a classic black hole and it somehow still existed, quantum data would be unable to climb up against infinite gravitational intensity to reach the surface of its event horizon and escape.

Hawking radiationHawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...

(so-far undetected particles and photons thought to be emitted from the proximity of black holes) would not circumvent the information paradox; it could reveal only the

massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

,

angular momentumIn physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

, and

electric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

of classic black holes. Hawking radiation is thought to be created when

virtual particleIn physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...

s— antiparticle pairs of all sorts plus photons, which are their own antiparticle—form very close to the event horizon and one member of a pair spirals in while the other escapes.

The fuzzball theory advanced by Mathur and Lunin satisfies the law of reversibility because the quantum nature of all the strings that fall into a fuzzball is preserved as new strings contribute to the fuzzball’s makeup; no quantum information is squashed out of existence. Moreover, this aspect of the theory is testable since its central tenet holds that a fuzzball’s quantum data do not stay trapped at its center but reaches up to its fuzzy surface and that Hawking radiation carries away this information, which is encoded in the delicate correlations between the outgoing quanta.

## See also

- Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

- Supermassive black hole
A supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...

- Black hole information paradox
The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...

- Black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...

- Degenerate matter
Degenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...

- Gravitational singularity
A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

- Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

- Quantum foam
Quantum foam, also referred to as spacetime foam, is a concept in quantum mechanics, devised by John Wheeler in 1955. The foam is supposed to be the foundations of the fabric of the universe. Additionally, it can be used as a qualitative description of subatomic spacetime turbulence at extremely...

- Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

- String (physics)
A string is a hypothetical vibrating one-dimensional sub-atomic structure and one of the main objects of study in string theory, a branch of theoretical physics. There are different string theories, many of which are unified by M-theory. A string is an object with a one-dimensional spatial extent,...

- String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

- Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...

- Timeline of black hole physics
Timeline of black hole physics* 1640 — Ismael Bullialdus suggests an inverse-square gravitational force law* 1684 — Isaac Newton writes down his inverse-square Law of universal gravitation...

## External links

- Are Black Holes Fuzzballs? — by Space Today Online
- Information paradox solved? If so, Black Holes are "Fuzzballs" — by Ohio State University
- The fuzzball paradigm for black holes: FAQ — by Samir D. Mathur
- arXiv.org link: Unwinding of strings thrown into a fuzzball — by Stefano Giusto and Samir D. Mathur
- Astronomers take virtual plunge into black hole (84 MB) (10 MB version)— 40-second animation produced by JILA, which is a joint venture of the University of Colorado at Boulder
The University of Colorado Boulder is a public research university located in Boulder, Colorado...

and the NISTThe National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

- The black hole information problem and the fuzzball proposal (I), CERN document
- The black hole information problem and the fuzzball proposal (II), CERN document
- The black hole information paradox and the fuzzball proposal (III), CERN document
- The black hole information problem and the fuzzball proposal (IV), CERN document