Fuzzball (string theory)
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Fuzzballs are hypothetical objects in
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 t ...
, intended to provide a fully quantum description of the
black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
s predicted by
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
. The fuzzball hypothesis dispenses with 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 outside 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 c ...
is actually an extended object: a ball of strings, which are advanced as the ultimate building blocks of matter and light. Under
string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
, strings are bundles of energy vibrating in complex ways in both the three familiar dimensions of space as well as in
extra dimensions In physics, extra dimensions or extra-dimensional spaces are proposed as additional space or time dimensions beyond the (3 + 1) typical of observed spacetime — meaning 5-dimensional or higher. such as the first attempts based on the K ...
.Jennifer Ouellette
"The Fuzzball Fix for a Black Hole Paradox"
''Quanta Magazine'', (June 23, 2015).
Fuzzballs provide resolutions to two major open problems in black hole physics. First, they avoid the
gravitational singularity A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by defini ...
that exists within the event horizon of a black hole. General relativity predicts that at the singularity, the curvature of spacetime becomes infinite, and it cannot determine the fate of matter and energy that falls into it. Physicists generally believe that the singularity is not a real phenomenon, and proposed theories of
quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...
, such as superstring theory, are expected to explain its true nature. Second, they resolve the black hole information paradox: the quantum information of matter falling into a black hole is trapped behind the event horizon, and seems to disappear from the universe entirely when the black hole evaporates due to
Hawking radiation Hawking radiation is black-body radiation released outside a black hole's event horizon due to quantum effects according to a model developed by Stephen Hawking in 1974. The radiation was not predicted by previous models which assumed that onc ...
. This would violate a fundamental law of quantum mechanics requiring that quantum information be conserved. As no direct experimental evidence supports either string theory in general or fuzzballs in particular, both are products purely of calculations and theoretical research.Joseph Conlon. "Why String Theory?", CRC Press, (2016), . However, the existence of fuzzballs may be testable through
gravitational-wave astronomy Gravitational-wave astronomy is a subfield of astronomy concerned with the detection and study of gravitational waves emitted by astrophysical sources. Gravitational waves are minute distortions or ripples in spacetime caused by the acceleration ...
."A Way to Experimentally Test String Theory's 'Fuzzball' Prediction"
APS Journals, (September 16, 2021).


Physical properties


String theory and composition

Samir D. Mathur of
Ohio State University The Ohio State University (Ohio State or OSU) is a public university, public Land-grant university, land-grant research university in Columbus, Ohio, United States. A member of the University System of Ohio, it was founded in 1870. It is one ...
published eight scientific papers between 2001 and 2012, assisted by postdoctoral researcher Oleg Lunin, who contributed to the first two papers. The papers propose that black holes are sphere-like extended objects with a definite volume and are composed of strings. This differs from the classic view of black holes in which there is a singularity at their centers, which are thought to be a zero-dimensional, zero-volume point in which the entire mass of a black hole is concentrated at infinite density, surrounded many kilometers away by an event horizon below which light cannot escape. All variations of string theory hold that the fundamental constituents of
subatomic particle In physics, a subatomic particle is a particle smaller than 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 baryon, lik ...
s, including the
force carrier In quantum field theory, a force carrier is a type of particle that gives rise to forces between other particles. They serve as the quanta of a particular kind of physical field. Force carriers are also known as messenger particles, intermedia ...
s (e.g.,
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 particles that can ...
s and
gluon A gluon ( ) is a type of Massless particle, massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a Spin (physi ...
s), are actually strings of energy that take on their identities and respective masses by vibrating in different modes and frequencies. The fuzzball concept is rooted in a particular variant of superstring theory called Type IIB (see also ''
String duality String duality is a class of symmetries in physics that link different string theories, theories which assume that the fundamental building blocks of the universe are strings instead of point particles. Overview Before the so-called "duality r ...
''), which holds that strings are both "open" (double-ended entities) and "closed" (looped entities) and that there are spacetime dimensions wherein five of the six extra spatial dimensions are "compactified".Samir D. Mathur. "A proposal to resolve the black hole information paradox"
ArXiv:hep-th/0205192
(May 19, 2002).
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 gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses ...
in which the neutrons have undergone a
phase transition In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic Sta ...
and decomposed, 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 ...
comprising them. Accordingly, fuzzballs are theorized to be the terminal phase of
degenerate matter Degenerate matter occurs when the Pauli exclusion principle significantly alters a state of matter at low temperature. The term is used in astrophysics to refer to dense stellar objects such as white dwarfs and neutron stars, where thermal press ...
. Mathur calculated that the physical surfaces of fuzzballs have radii equal to that of the event horizon of classic black holes; thus, the
Schwarzschild radius The Schwarzschild radius is a parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius of a sphere in flat space that has the same surface area as that of the event horizon of a Schwarzschild black ho ...
of a ubiquitous 6.8 
solar mass The solar mass () is a frequently used unit of mass in astronomy, equal to approximately . It is approximately equal to the mass of the Sun. It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxie ...
() stellar-mass-class black hole—or fuzzball—is 20 kilometers when the effects of spin are excluded. He also determined that the event horizon of a fuzzball would, at a very tiny scale (likely on the order of a few
Planck length In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: '' c'', '' G'', '' ħ'', and ''k''B (described further below). Expressing one of ...
s), be very much like a mist: fuzzy, hence the name "fuzzball." 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 an object to escape from contact with or orbit of a primary body, assuming: * Ballistic trajectory – no other forces are acting on the object, such as ...
exceeds the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
—a realm devoid of all structure. Moreover, precisely at the singularity—the heart of a classic black hole—spacetime itself is thought to break down catastrophically since infinite density demands infinite escape velocity; such conditions are problematic with known physics. Under the fuzzball premise, however, the strings comprising matter and photons are believed to fall onto and absorb into the fuzzball's surface, which is located at the event horizon—the threshold at which the escape velocity has achieved the speed of light. A fuzzball ''is'' a black hole; spacetime, photons, and all else 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 diverge only at the quantum level; that is, classic black holes and fuzzballs differ only in their internal composition and 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, which allows the virtual particles to spontaneously emer ...
s that form close to their event horizons (see ', below). Fuzzballs are thought by their proponents to be the true quantum description of black holes.


Densities

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'', or join. 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 vibration modes, relaxing to considerable lengths. The string theory formulas of Mathur and Lunin produce fuzzball surface 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-r ...
calculated using an entirely different mathematical technique 87 years earlier. Since the volume of fuzzballs is a function of the Schwarzschild radius (2953 meters per for a non-rotating black hole), 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 an average, or 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 non-spinning fuzzball the size of a drop of water would, on average, have a mass of twenty million metric tons, which is equivalent to that of a granite ball 243 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 extreme—about the same as neutron stars—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. Since the mean densities of fuzzballs (and the effective densities of classic black holes) decrease as the inverse square of their mass, fuzzballs greater than are actually less dense than neutron stars possessing the minimum possible density. Due to the mass-density inverse-square rule, fuzzballs need not even have unimaginable densities.
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 ...
s, which are found at the center of virtually all galaxies, can have modest densities. For instance,
Sagittarius A* Sagittarius A*, abbreviated as Sgr A* ( ), is the supermassive black hole at the Galactic Center of the Milky Way. Viewed from Earth, it is located near the border of the constellations Sagittarius and Scorpius, about 5.6° south o ...
, the black hole at the center of our Milky Way galaxy, is 4.3 million . The fuzzball model predicts that a non-spinning supermassive black hole with the same mass as Sagittarius A* has a mean density "only" 51 times that of gold. Moreover, at 3.9 billion (a rather large super-massive black hole), a non-spinning fuzzball would have a radius of 77
astronomical unit The astronomical unit (symbol: au or AU) is a unit of length defined to be exactly equal to . Historically, the astronomical unit was conceived as the average Earth-Sun distance (the average of Earth's aphelion and perihelion), before its m ...
s—about the same size as the termination shock 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).Vttoth.com
Hawking radiation calculator


Neutron star collapse

Black holes (or fuzzballs) are produced in various ways, most of which are exceedingly violent mass-shedding events like
supernova A supernova (: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last stellar evolution, evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion ...
s,
kilonova A kilonova (also called a macronova) is a transient astronomical event that occurs in a compact star, compact binary system when two neutron stars (BNS) or a neutron star and a black hole collide. The kilonova, visible over the weeks and months ...
s, and
hypernova A hypernova is a very energetic supernova which is believed to result from an extreme core collapse scenario. In this case, a massive star (>30 solar masses) collapses to form a rotating black hole emitting twin astrophysical jets and surrounded b ...
s. However, an accreting neutron star (one slowly siphoning off mass from a companion star) that exceeds a critical mass limit, ''M''max, will suddenly and nonviolently (relatively speaking) collapse into a black hole or fuzzball. Such a collapse can serve as a helpful case study when examining the differences between the physical properties of neutron stars and fuzzballs. Neutron stars have a maximum possible mass, known as the
Tolman–Oppenheimer–Volkoff limit The Tolman–Oppenheimer–Volkoff limit (or TOV limit) is an upper bound to the mass of cold, non-rotating neutron stars, analogous to the Chandrasekhar limit for white dwarf stars. Stars more massive than the TOV limit collapse into a black hol ...
; this limit is not precisely known, but it is believed to lie between and . If a neutron star exceeds this mass,
neutron degeneracy pressure Degenerate matter occurs when the Pauli exclusion principle significantly alters a state of matter at low temperature. The term is used in astrophysics to refer to dense stellar objects such as white dwarfs and neutron stars, where thermal pressu ...
can no longer resist the force of gravity and it will rapidly collapse until some new physical process takes over. In classical general relativity, the collapsing neutron star reaches a critical density and forms an event horizon; to the outside universe it becomes a black hole, and the collapse proceeds towards a gravitational singularity. In the fuzzball model, the
hadron In particle physics, a hadron is a composite subatomic particle made of two or more quarks held together by the strong nuclear force. Pronounced , the name is derived . They are analogous to molecules, which are held together by the electri ...
s in its core (neutrons and perhaps a smattering of protons and
meson In particle physics, a meson () is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, the ...
s) decompose into what could be regarded as the final stage of degenerate matter: a ball of strings, which the fuzzball model predicts is the true quantum description of not only black holes but theorized quark stars composed of
quark matter Quark matter or QCD matter ( quantum chromodynamic) refers to any of a number of hypothetical phases of matter whose degrees of freedom include quarks and gluons, of which the prominent example is quark-gluon plasma. Several series of conferences ...
.


Information paradox

Classical black holes create a problem for physics known as the ''black hole information paradox''; there is no such paradox under the fuzzball hypothesis. The paradox was first raised in 1972 by
Jacob Bekenstein Jacob David Bekenstein (; May 1, 1947 – August 16, 2015) was a Mexican-born American-Israeli theoretical physicist who made fundamental contributions to the foundation of black hole thermodynamics and to other aspects of the connections betwee ...
and later popularized by
Stephen Hawking Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...
. The information paradox is born of a requirement of quantum mechanics that quantum information ''must be conserved'', which conflicts with general relativity's requirement that if black holes have singularities at their centers, quantum information ''must be extinguished'' from spacetime. This paradox can be viewed as a contradiction between two very different theories: general relativity, which describes the largest gravity-based phenomena in the Universe, and quantum mechanics, which describes the smallest phenomena. Fuzzball theory purports to resolve this tension because the Type IIB superstring theory it is based on is a quantum description of gravity called
supergravity In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...
. A black hole that fed primarily on the stellar atmosphere (protons, neutrons, and electrons) of a nearby companion star should, if it obeyed the known laws of quantum mechanics, grow to have a quantum composition different from another black hole that fed only on light (photons) from neighboring stars and the
cosmic microwave background The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dar ...
. This follows a core precept of both classical and quantum physics that, ''in principle'', the state of a system at one point in time should determine its state at any other time. Yet, general relativity's implications for classic black holes are inescapable: Other than the fact that the two black holes would become increasingly massive due to the infalling matter and light, no difference in their quantum compositions would exist because if singularities have zero volume, black holes ''have no'' quantum composition. Moreover, even if quantum information was not extinguished at singularities, it could not climb against infinite gravitational intensity and reach up to and beyond the event horizon where it could reveal itself in normal spacetime. This is called the
no-hair theorem The no-hair theorem states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent ''externally'' observabl ...
, which states that black holes can reveal nothing about themselves to outside observers except their
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
,
angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
, and
electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...
, whereby the latter two could theoretically be revealed through a phenomenon known as
superradiance In physics, superradiance, or superradiation, is the radiation enhancement effects in several contexts including quantum mechanics, astrophysics and relativity. Quantum optics In quantum optics, superradiance is a phenomenon that occurs when a ...
.
Stephen Hawking Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...
showed that quantum effects will make black holes appear to be blackbody radiators with
effective temperature The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature ...
s inversely proportional to the mass of a black hole. This radiation, now called
Hawking radiation Hawking radiation is black-body radiation released outside a black hole's event horizon due to quantum effects according to a model developed by Stephen Hawking in 1974. The radiation was not predicted by previous models which assumed that onc ...
, cannot circumvent the no-hair theorem as it can reveal only a black hole's mass. For all practical purposes, Hawking radiation is undetectable (see §'' Testability of the theory'', below). In a purely theoretical sense, the fuzzball theory advanced by Mathur and Lunin goes beyond Hawking's formula relating the blackbody temperature of Hawking radiation and the mass of the black hole emitting it. Fuzzball theory satisfies the requirement that quantum information be conserved because it holds, in part, that the quantum information of the strings that fall onto a fuzzball is preserved as those strings dissolve into and contribute to the fuzzball's quantum makeup. The theory further holds that a fuzzball's quantum information is not only expressed at its surface but tunnels up through the tunneling fuzziness of the event horizon where it can be imprinted on Hawking radiation, which very slowly carries that information into regular spacetime in the form of delicate correlations in the outgoing quanta. Fuzzball theory's proposed solution to the black hole information paradox resolves a significant incompatibility between quantum mechanics and general relativity. At present, there is no widely accepted theory of
quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...
—a quantum description of gravity—that is in harmony with general relativity. However, all five variations of superstring theory, including the Type IIB variant upon which fuzzball theory is based, have quantum gravity incorporated into them. Moreover, all five versions have been hypothesized as actually constituting five different limits, or subsets, that are unified under
M-theory In physics, M-theory is a theory that unifies all Consistency, consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1 ...
.


Testability of the theory

As no direct experimental evidence supports either string theory or fuzzball theory, both are products purely of calculations and theoretical research. However, theories must be experimentally testable if there is to be a possibility of ascertaining their validity. To be in full accordance with the
scientific method The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and ...
and one day be widely accepted as true—as are Einstein's theories of special and general relativity—theories regarding the natural world must make predictions that are consistently affirmed through observations of nature. Superstring theory predicts the existence of highly elusive particles that, while they are actively being searched for, have yet to be detected. Moreover, fuzzball theory cannot be substantiated by observing its predicted subtle effects on Hawking radiation because the radiation itself is for all practical purposes undetectable.Alastair Gunn
"What is Hawking radiation?"
BBC Science Focus, (April 16, 2022).
However, fuzzball theory may be testable through
gravitational-wave astronomy Gravitational-wave astronomy is a subfield of astronomy concerned with the detection and study of gravitational waves emitted by astrophysical sources. Gravitational waves are minute distortions or ripples in spacetime caused by the acceleration ...
. The first challenge insofar as the testability of fuzzball theory is it is rooted in unproven ''superstring theory'', which is short for ''supersymmetric string theory.''
Supersymmetry Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...
predicts that for each known quanta (particle) in the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
, a
superpartner In particle physics, a superpartner (also sparticle) is a class of hypothetical elementary particles predicted by supersymmetry, which, among other applications, is one of the well-studied ways to extend the Standard Model of high-energy physics. ...
particle exists that differs by
spin Spin or spinning most often refers to: * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin quantum number, a number which defines the value of a particle's spin * Spinning (textiles), the creation of yarn or thr ...
. This means that for every
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 half odd-intege ...
(massless particles in the Standard Model with integer spins like 0, 1, and 2), there is a supersymmetric-spin
fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
-like particle known as a gaugino that has a half-odd-integer spin (e.g., and ) and possesses a rest mass. Examining this spin- supersymmetry in the opposite direction, superstring theory predicts that fermions from the Standard Model have boson-like superpartners known as sfermions, except that unlike actual gauge bosons from the Standard Model, sfermions don't strongly act as
force carrier In quantum field theory, a force carrier is a type of particle that gives rise to forces between other particles. They serve as the quanta of a particular kind of physical field. Force carriers are also known as messenger particles, intermedia ...
s."Supersymmetry"
CERN/Science/Physics.
All bosons (e.g., photons) and the boson-like sfermions will readily overlap each other when crowded, whereas fermions and the fermion-like gauginos possessing mass (such as electrons, protons, and quarks) will not; this is one reason why superpartners—if they exist—have properties that are exceedingly different from their Standard Model counterparts. Take the example of the photon, which is a massless boson with an integer spin of 1 and is the carrier of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
in the Standard Model; it is predicted to have a superpartner called a photino, which is a mass-carrying fermion with a half-odd-integer spin of . Conversely, the electron (spin ) is an example of a mass-carrying fermion where its superpartner is the spin-0 selectron, which is a massless boson but is not considered to be a primary force carrier. The experimental detection of superpartners would not only bolster superstring theory but would also help fill gaps in current particle physics, such as the likely composition of
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
and the muon's anomalous magnetic moment (it should be precisely equal to 2 and is instead about , suggesting hidden interactions); particle physicists have accordingly been searching for these superpartners. Based on cosmological effects, there is strong evidence for the existence of dark matter of ''some'' sort (see '' Dark matter: Observational evidence''), but if it is composed of subatomic particles, those particles have proven to be notoriously elusive despite the wide variety of detection techniques that have been employed since 1986. This difficulty in detecting supersymmetric particles is not surprising to particle physicists since the lightest ones are believed to be stable, electrically neutral, and interact weakly with the particles of the Standard Model. Though many searches using particle colliders have ruled out certain mass ranges for supersymmetric particles, the hunt continues. Fuzzball theory resolves a long-standing conflict between general relativity and quantum mechanics by holding that quantum information is preserved in fuzzballs and that Hawking radiation originating within the Planck-scale
quantum foam Quantum foam (or spacetime foam, or spacetime bubble) is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at this small scale, particles of matter and antimatter are constantl ...
just above a fuzzball's surface is subtly encoded with that information. As a practical matter, however, Hawking radiation is virtually impossible to detect because black holes emit it at astronomically low power levels and the individual photons constituting Hawking radiation have extraordinarily little energy. This underlies why theoretically perfectly quiescent black holes (ones in a universe containing no matter or other types of electromagnetic radiation to absorb) evaporate so slowly as they lose energy (and equivalent amounts of mass) via Hawking radiation; even a modest black hole would require times the current age of the Universe to vanish. Moreover, a top-of-the-list supermassive black hole would require ten million-trillion-trillion times longer still to evaporate: times the age of the Universe. Hawking showed that the energy of photons released by Hawking radiation is inversely proportional to the mass of a black hole and, consequently, the smallest black holes emit the most energetic photons that are the least difficult to detect. However, the radiation emitted by even a minimum-size, black hole (or fuzzball) comprises extremely low-energy photons that are equivalent to those emitted by a
black body A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The radiation emitted by a black body in thermal equilibrium with its environment is ...
with a temperature of around 23 billionths of one
kelvin The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...
above
absolute zero Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 ° ...
. More challenging still, such a black hole has a radiated power—for the ''entire'' black hole—of (billion-billionths of one milliwatt). Such an infinitesimal transmitted power is to one watt as th of a drop of water (about one-quarter the volume of a typical grain of table salt) is to all the Earth's oceans. Critically though, when signals are this weak, the challenge is no longer one of classic radio astronomy technological issues like gain and
signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in deci ...
; Hawking radiation comprises individual photon quanta, so such a weak signal means a black hole is emitting at most only ten photons per second. Even if such a black hole was only 100 lightyears away, the odds of just one of its Hawking radiation photons landing anywhere on Earth—let alone being captured by an antenna—while a human is watching are astronomically improbable. Importantly, the above values are for the smallest possible stellar-mass black holes; far more difficult yet to detect is the Hawking radiation emitted by supermassive black holes at the center of galaxies. For instance, M87* which is an unremarkable supermassive black hole, emits Hawking radiation at a near-nonexistent radiant power of at most 13 photons per century and does so with a wavelength so great that a receiving antenna possessing even a modest degree of absorption efficiency would be larger than the Solar System. However, fuzzball theory may be testable through gravitational-wave astronomy. Gravitational wave observatories like the
Laser Interferometer Gravitational-Wave Observatory The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Prior to LIG ...
(LIGO) have proven to be a revolutionary advancement in astronomy and are enabling astronomers and theoretical physicists to develop ever-more detailed insights into compact objects such as neutron stars and black holes. Ever since the first direct detection of gravitational waves, a 2015 event known as
GW150914 The first direct observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016. Previously, gravitational waves had been inferred only indirectly, via their effect on t ...
, which was a merger between a binary pair of stellar-mass black holes, gravitational-wave signals have so far matched the predictions of general relativity for classical black holes with singularities at their centers. However, an Italian team of scientists that ran computer simulations suggested in 2021 that existing gravitational-wave observatories are capable of discerning fuzzball-theory-supporting evidence in the signals from merging binary black holes (and the resultant effects on ringdowns) by virtue of the nontrivial unique attributes of fuzzballs, which are extended objects with a physical structure. The team's simulations predicted slower-than-expected decay rates for certain vibration modes that would also be dominated by "echoes" from earlier ring oscillations. Moreover, a separate Italian team a year earlier posited that future gravitational-wave detectors, such as the proposed
Laser Interferometer Space Antenna The Laser Interferometer Space Antenna (LISA) is a planned space probe to detect and measure gravitational waves—tiny ripples in the fabric of spacetime—from astronomical sources. LISA will be the first dedicated space-based gravitational-w ...
(LISA), which is intended to have the ability to observe high-mass binary mergers at frequencies far below the limits of current observatories, would improve the ability to confirm aspects of fuzzball theory by orders of magnitude."Phenomenological Imprints of the String-Theory 'Fuzzball' Scenario"
University of Rome–La Sapienza, (November 24, 2020).


References


External links



– Space Today Online
The Fuzzball Fix for a Black Hole Paradox
June 23, 2015 – Quanta Magazine

– The Ohio State University * ArXiv.org link
Unwinding of strings thrown into a fuzzball
– Stefano Giusto and Samir D. Mathur
Astronomers take virtual plunge into black hole (84 MB)10 MB version
, a 40-second animation produced by JILA – a joint venture of the
University of Colorado at Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a Public university, public research university in Boulder, Colorado, United States. Founded in 1876, five months before Colorado became a Federated state, state, it is the fla ...
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 s ...
* Video lecture series at CERN (four parts approximately an hour each)
"The black hole information problem and the fuzzball proposal", Part 1Part 2Part 3Part 4
{{Black holes String theory Black holes Hypothetical stars Stellar black holes Gravitational singularities