Fuzzballs are theorized by some

superstring theory Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string the ...

scientists to be the true

quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...

description of

black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...

s. The theory attempts to resolve two intractable problems that classic black holes pose for modern physics: # The information paradox wherein the quantum information bound in in-falling 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 at the heart of the black hole, where conventional black hole theory says there is infinite

spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...

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.The smallest linear dimension in physics that has any meaning in the measurement of spacetime is the Planck length, which is
CODATA value
. Below the Planck length, the effects of

quantum foam Quantum foam or spacetime foam is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at these small scales, particles of matter and antimatter are constantly created and destroye ...

dominate and it is meaningless to conjecture about length at a finer scale—much like how meaningless it would be to measure ocean tides at a precision of one centimeter in storm-tossed seas. A singularity is thought to have a diameter that does not amount to even one Planck length; which is to say, 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 horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact ob ...

is actually a ball of strings, 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

(also known as ''spacetime foam'').

Physical characteristics

Samir D. Mathur of

Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best public ...

, 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 singularity, which the classic view holds to be a zero-dimensional, zero-volume point into which a black hole's entire mass is concentrated.''AdS/CFT duality and the black hole information paradox'', SD Mathur and Oleg Lunin, Nuclear Physics B, 623, (2002),
arxiv
; and ''Statistical interpretation of Bekenstein entropy for systems with a stretched horizon'', SD Mathur and Oleg Lunin, Physical Review Letters, 88 (2002)
arxiv
. String theory holds that the fundamental constituents of

subatomic particle In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a prot ...

s, including the

force carrier In quantum field theory, a force carrier, also known as messenger particle or intermediate particle, is a type of particle that gives rise to forces between other particles. These particles serve as the quanta of a particular kind of physical fiel ...

s (e.g.

boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always m ...

s, and

gluon A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind q ...

s), are all composed of 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 star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. whit ...

where its neutrons have decomposed, or "melted", liberating the

quarks A quark () is a type of 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. All commonly o ...

(strings in string theory) composing them. Accordingly, fuzzballs can be regarded as the most extreme form of

degenerate matter Degenerate matter is a highly dense state of fermionic matter in which the Pauli exclusion principle exerts significant pressure in addition to, or in lieu of, thermal pressure. The description applies to matter composed of electrons, protons, neu ...

. Whereas the

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 radius The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristi ...

for a median-size

stellar-mass black hole A stellar black hole (or stellar-mass black hole) is a black hole formed by the gravitational collapse of a star. They have masses ranging from about 5 to several tens of solar masses. The process is observed as a hypernova explosion or as a ga ...

of 6.8

solar mass The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass o ...

es () is 20 kilometers. With classical-model 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 velocity In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non- propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically s ...

exceeds the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for ...

. 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 are not able to be computed with a divisor of zero. With the fuzzball model, however, the strings comprising an object are believed to simply fall onto and absorb into the surface of the fuzzball, which corresponds to the

—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 the classical model of black holes featuring a singularity at its center. The two theories differ only at the quantum level; that is, they differ only in their internal composition as well as how they affect

virtual particle A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbat ...

s that form close to their event horizons (see , 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 m per ), 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 fuzzball would have a mean density of .This is a mean bulk density; as with neutron stars, the sun, and its planets, a fuzzball's density varies from the surface where it is less dense, to its center where it is most dense. 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.Smaller fuzzballs would be denser yet. The smallest black hole yet discovered, XTE J1650-500, is . Theoretical physicists believe that the transition point separating neutron stars and black holes is 1.7 to 2.7 (Goddard Space Flight Center:
NASA Scientists Identify Smallest Known Black Hole
'). A very small, fuzzball would be over six times as dense as a median-size fuzzball of 6.8 , with a mean density of . A bit of such a fuzzball the size of a drop of water would have a mass of 126 million metric tons, which is the mass of a granite ball 449 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

s.Neutron stars have a mean density thought to be in the range of which is equal to median-size fuzzballs ranging from 7.1 to 5.6 . However, the smallest fuzzballs are denser than neutron stars; a small, fuzzball would be four to seven times denser than a neutron star. On a "teaspoon" (≈4.929 mL) basis, which is a common measure for conveying density in the popular press to a general-interest readership, comparative mean densities are as follows: * fuzzball: 12.45 billion metric tons per teaspoon * fuzzball: 1.963 billion metric tons per teaspoon * Neutron star: 1.8–2.9 billion metric tons per teaspoon.—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 are not 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 Schwarzschild Karl Schwarzschild (; 9 October 1873 – 11 May 1916) was a German physicist and astronomer. Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non ...

calculated using an entirely different mathematical technique 87 years earlier. Due to the mass-density inverse-square rule, fuzzballs need not all have unimaginable densities. There are also

supermassive black hole A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions of times the mass of the Sun (). Black holes are a class of astronomical ob ...

s, which are found at the center of virtually all galaxies.

Sagittarius A* Sagittarius A* ( ), abbreviated Sgr A* ( ), is the supermassive black hole at the Galactic Center of the Milky Way. It is located near the border of the constellations Sagittarius and Scorpius, about 5.6° south of the ecliptic, vi ...

, the black hole at the center of our Milky Way galaxy, is 4.3 million . If fuzzball theory is correct, it has a mean density that is "only" 51 times that of gold. At 3.9 billion (a rather large super-massive black hole), a fuzzball would have a radius of 77

astronomical unit The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits ...

s—about the same size as the

termination shock The heliosphere is the magnetosphere, astrosphere and outermost atmospheric layer of the Sun. It takes the shape of a vast, bubble-like region of space. In plasma physics terms, it is the cavity formed by the Sun in the surrounding interstell ...

of the Solar System's heliosphere—and a mean density equal to that of the Earth's atmosphere at sea level (1.2 kg/m³). 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.The "speed of light" in this context is from the point of view of an observer who is traveling along with the fuzzball and is at the edge of its gravitational sphere of influence. The escape velocity is ''precisely'' equal to (not "very close to") the speed of light because one is not measuring the velocity of photons or particles with respect to spacetime, but instead observing a region of spacetime that has been warped the maximum permissible extent with respect to itself. From a Newtonian point of view, infalling objects are achieving a velocity that—to certain external observers—appears to be precisely equal to the speed of light at the point the objects encounter a black hole's event horizon. From Einstein's point of view, the infalling energy and matter are merely following the contours of spacetime up to the point spacetime becomes maximally warped. 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 Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

, via his

special theory of relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws ...

, 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

Classical black holes create a problem for physics known as the

black hole information paradox The black hole information paradox is a puzzle that appears when the predictions of quantum mechanics and general relativity are combined. The theory of general relativity predicts the existence of black holes that are regions of spacetime from wh ...

, an issue first raised in 1972 by

Jacob Bekenstein Jacob David Bekenstein ( he, יעקב בקנשטיין; May 1, 1947 – August 16, 2015) was an American and Israeli theoretical physicist who made fundamental contributions to the foundation of black hole thermodynamics and to other aspects of ...

and later popularized by Stephen Hawking. The information paradox is born 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 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. As the study of the statistical mechanics of black-body radiation led to the development ...

. 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 radiation Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical arg ...

(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

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementa ...

angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syste ...

, and

electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectiv ...

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

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, carrying away the energy of the black hole. 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 reach up to its fuzzy surface and that Hawking radiation carries away this information, which is encoded in the delicate correlations between the outgoing quanta.

Notes and references

External links

Are Black Holes Fuzzballs?
— by Space Today Online

— by The 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 JILA, formerly known as the Joint Institute for Laboratory Astrophysics, is a physical science research institute in the United States. JILA is located on the University of Colorado Boulder campus. JILA was founded in 1962 as a joint institute of ...

, which is a joint venture of the

University of Colorado at Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado syst ...

and the

NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...

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

- by Jennifer Ouellete {{Star String theory Black holes Hypothetical stars Stellar black holes

Physical characteristics

Information paradox

See also

Notes and references

External links