Fuzzball (string theory)
Fuzzball theory, which is derived from superstring theory, is advanced by its proponents as a description of black holes that harmonizes quantum mechanics and Albert Einstein's general theory of relativity, which have long been incompatible. Fuzzball theory dispenses with the singularity at the heart of a black hole by positing that the entire region within the black hole's event horizon is actually an extended object: a ball of strings, which are advanced as the ultimate building blocks of matter and light. Under string theory, strings are 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 foam (see Fig. 2, below). Fuzzball theory addresses two intractable problems that classic black hole theory poses for modern physics:

 It dispenses with the gravitational singularity at the heart of the black hole, which is thought to be surrounded by an event horizon, the inside of which is detached from the space and time—spacetime—of the rest of the universe (see  Conventional black hole theory holds that a singularity is a zero-dimensional, zero-volume point in which all of a black hole's mass exists at infinite density. Modern physics breaks down under such extremes because gravity would be so intense that spacetime itself breaks down catastrophically. It resolves the black hole information paradox wherein conventional black hole theory holds that the quantum information describing the light and matter that falls into a classic black hole is thought to either be extinguished at singularities, or is somehow preserved within singularities but the quantum information cannot climb up against the infinite gravitational intensity inside a black hole to reach past the event horizon so it is visible to regular spacetime. Either situation violates a fundamental law of quantum mechanics requiring that quantum information be conserved. Physical properties

String theory and composition  
Samir D. Mathur of The Ohio State University published six scientific papers between 2001 and 2012 (along with postdoctoral researcher Oleg Lunin for the first two papers) proposing 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 (see , 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 variants of string theory hold that the fundamental constituents of subatomic particles, including the force carriers (e.g. bosons, photons, and gluons), are actually strings of energy that take on their identities and respective masses by vibrating in different modes and/or frequencies. Fuzzball theory is rooted in a particular variation of superstring theory called Type IIB, which holds that there are  spacetime dimensions wherein five of the six extra spatial dimensions are "compactified" (see 

Unlike the view of a black hole as a singularity, a small fuzzball can be thought of as an extra-dense neutron star in which the neutrons have undergone a phase transition and decomposed, liberating the quarks (strings in string theory) comprising them. Accordingly, fuzzballs are theorized to be the terminal phase of degenerate matter. Mathur calculated that the physical surface of fuzzballs have radii equal to that of the event horizon of classic black holes; thus, the Schwarzschild radius of a ubiquitous 6.8 solar mass () 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 an extremely small scale (likely on the order of a few Planck lengths), 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 exceeds the speed of light—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 theory, however, the strings comprising matter and photons are believed to fall onto and absorb into the surface of the fuzzball, 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 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 diverge only at the quantum level; that is, classic black holes and fuzzballs differ only in their internal composition as well as how they affect virtual particles 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. 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 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 string theory formulas of Mathur and Lunin produce fuzzball surface radii that precisely equal Schwarzschild radii, which Karl Schwarzschild 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 (Fig. 3 ). 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 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. As shown in Fig. 4 below, neutron stars (the pink stripe) exist only in a narrow range of masses, beginning at the theoretical minimum known as the Chandrasekhar limit of  and extending up to , which is the theoretical maximum value at which neutron stars must collapse into either black holes or fuzzballs. If, for example, the precise transition point proved one day to be  (the double-ended red arrow), then an accreting neutron star that reached that limit will have accumulated more matter than neutron degeneracy pressure and other phenomena can resist and will experience a sudden cascading collapse. In doing so according to fuzzball theory, its neutrons (and perhaps a smattering of protons) decompose into what could be regarded as the final stage of degenerate matter: a ball of strings, which fuzzball theory predicts is the true quantum description of not only black holes, but theorized quark stars composed of quark matter. Though black holes (and fuzzballs) are produced in a variety of ways, many of which are exceedingly violent mass-shedding events like supernovas, the collapse of an accreting  neutron star, which is already a supernova remnant, can quietly produce a fuzzball with the same mass but with a radius of only 7.32 kilometers (reduced from around 13.5 kilometers) and with a density that increased six-fold, from roughly  to . As can also be seen in Fig. 4, because the mean densities of fuzzballs (and the effective densities of classic black holes) decrease as the inverse square of 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 all have unimaginable densities. Supermassive black holes, which are found at the center of virtually all galaxies, can have modest densities. For instance, Sagittarius A*, the black hole at the center of our Milky Way galaxy, is 4.3 million . Fuzzball theory 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 units—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). Escape velocity 

Irrespective of a fuzzball's mass, resultant mean density, or even its spin (which affects the Schwarzschild radius; see also Ergosphere and Rotating black hole), its physical surface is located exactly at the event horizon, which is the threshold at which the escape velocity equals the speed of light: 299,792,458 meters per second. Escape velocity, as its name suggests, is the velocity a smaller body must achieve to escape from a much more massive one; at 11,186 m/s, Earth's escape velocity is only 3.7 thousandths of one percent that of event horizons. Thus, event horizons—those either surrounding singularities or the surface of fuzzballs—lie at the point where spacetime, as shown in Fig. 5 at right, has been curved by gravity to the speed of light in accordance with general relativity. Gravitational acceleration 
Note that escape velocity, which has the unit of measure m/s, is distinct from gravitational strength, which is a different property known as acceleration and has m/s2 as its unit of measure. Though the escape velocity at an event horizon is a finite value (the speed of light), the gravitational strength at event horizons (and the surface of theorized fuzzballs) is infinite, which imbues particles possessing any mass whatsoever with infinite weight. Thus, an imaginary uncrushable rocket with its center of mass located at an event horizon would require infinite thrust to merely hover. This is general relativity's "accelerating frame of reference" counterpart to special relativity's requirement that infinite energy is required to accelerate an object possessing mass—even a subatomic particle—to precisely the speed of light. This property of infinite gravitational acceleration (infinite gravitational strength) at event horizons merits further scrutiny because at least as recently as 2023, online popular culture sites such as physics discussion boards, science websites, and even a university physics professor on YouTube writing calculations on a blackboard were promulgating a misunderstanding that objects have non-infinite weights at event horizons. The root cause of some of this misunderstanding was the improper application of Isaac Newton's -year-old formula for the law of universal gravitation (upper equation, below) rather than a proper appreciation of the ramifications of Einstein's theory of general relativity and how extreme gravity affects spacetime. Such a mistake is born of a logical non sequitur that while general relativity explains the existence of an event horizon around a black hole, that event horizon somehow remains part of regular un-warped spacetime where Newton's law of universal gravitation applies; it does not. In accordance with general relativity (lower equation, below), event horizons exist because their escape velocity equals the speed of light and gravitational acceleration is infinite, completely cutting them off from spacetime; no further calculations are warranted. Newton's law of universal gravitation: 
 Schwarzschild radius: 

Newton's law of universal gravitation yields increasingly inaccurate results as both space and time (spacetime) are increasingly warped by large masses. Even in the mildly gravitationally warped spacetime surrounding Earth, general relativity's gravitational effect on GPS satellites makes their onboard atomic clocks run 45,685 nanoseconds per day (0.01669 second per year) faster when in orbit versus their Earth-centered reference location, 26,562 kilometers below. To make GPS timing signals run at the slower center-of-Earth rate while in orbit, the satellites' reference oscillators receive a "factory offset" before launch, which also compensates for a smaller opposing effect of special relativity due to orbital velocity. At the other extreme, the improper use of Newton's formula to calculate the gravitational strength at the event horizon of the largest known supermassive black hole, Phoenix A* (see List of most massive black holes), which is estimated to be , yields a wildly incorrect (and even survivable) gravitational acceleration of only about 15 times that of Earth's gravity. Regardless of the size of a black hole, from the perspective of an observer outside a black hole's gravitational influence, the escape velocity at event horizons and the surface of fuzzballs equals the speed of light, gravitational strength is infinite, and the flow of time has come to a halt. Gravitational tides 
The aforementioned phenomenon of infinite gravitational acceleration at event horizons is distinct from gradients known as gravitational tides. The intense gravitational tides of stellar-mass black holes, intermediate-mass black holes, and smaller supermassive black holes cause a stretching effect on objects known as spaghettification, lethal amounts of which can occur hundreds of kilometers above the surface of stellar-mass fuzzballs (or above the event horizon surrounding a singularity). For instance, a 10  stellar-class fuzzball has a gravitational tide at its surface of 100 billion Earth-gravities per meter, which would stretch an infalling astronaut into a stream of paste well before reaching its surface. Even a relatively small 400,000  supermassive fuzzball, which has a gravitational tide of 64 Earth-gravities per meter at its surface, would pull apart the body of a hapless astronaut falling feet-first before reaching its surface due to vertebral tensile forces greater than the weight of one metric ton on Earth. Information paradox 

Classical black holes create a problem for physics known as the black hole information paradox; there is no such paradox under fuzzball theory. The paradox was first raised in 1972 by Jacob Bekenstein and later popularized by Stephen Hawking. The information paradox is born of a requirement of quantum mechanics that quantum information must be conserved, which is in conflict 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 on which it is based is a quantum description of gravity called supergravity. 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. 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 would be unable to 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, which states that general relativity requires that classic black holes with singularities at their centers can reveal nothing to the outside world regarding what went into them. Hawking radiation (undetectable radiation comprising photons and possibly other quanta thought to be emitted from the proximity of black holes) would not resolve the no-hair theorem for classic black holes with singularities; it could reveal only black hole mass, angular momentum, and electric charge. Hawking radiation is created whenever massless and truly neutral virtual particle pairs—virtual photons for modern expositions of this topic—form in proximity to, but outside of, an event horizon. One member of a virtual particle pair possesses negative mass-energy (in the absolute  sense), the other has positive mass-energy, and the average pair's net energy is zero.<ref group="Note">The meanings of "negative mass-energy” or simply "negative energy" (in the absolute  sense) in discussions of virtual photons at black holes, differs somewhat from what "negative energy" normally means for virtual photons in the lab (in regular spacetime). Virtual photons are oscillations in the background electromagnetic field that prevent an otherwise pure vacuum from containing (possessing) zero energy. Virtual photons are characterized by their wavelength (frequency, or "color"), momentum (which, unlike real photons, is exceedingly variable), and polarization (spin-angular momentum).</p>Unfortunately, terms like "negative energy," "antiparticle," and "antimatter" can add confusion to a topic that has long fallen victim to popular misunderstanding. Moreover, the issue of whether photons are best described as "waves" or "particles" can needlessly belabor a simple and accessible exposition on Hawking radiation if not formally addressed. Accordingly, a short treatise on the broad subject is required to establish context for how Hawking radiation can be viewed as "arising from virtual photons possessing negative energy tunneling through an event horizon. "The "wave–particle duality" adds complexity to a topic that is already challenging to understand. This duality is commonly encountered when photons are referred to as "quantized wave packets propagating in the electromagnetic field," rather than simply "particles." Referring to photons as "particles" more accurately and conveniently describes the nature of photons after they hit a light detector in a double-slit experiment; it is needlessly ponderous to say "the photon's wave function then collapses to a point." Especially in a treatise on Hawking radiation, where Hawking himself wrote, "there will be pairs of particles, one with negative energy and one with positive energy," it is very useful here to use particle-based vernacular. Nonetheless, the wave nature of virtual photons must be addressed to properly cover Hawking radiation.Though one member of a pair of virtual photons can possesses negative energy, this is neither the product of charge conjugation (the reversing of electric charge as permitted by  nor is it antimatter because, by definition, antimatter is "matter (which has mass) possessing an electric charge opposite that of ordinary matter." Though photons are considered to be their own antiparticle (which is a broad family that confusingly includes antimatter like antiprotons), photons are more specifically a truly neutral particle / antiparticle. Furthermore, real photons must always possess energy equal to the speed of light times their momentum vector and must have zero rest mass.In laboratories, virtual photons possess different kinds of momentum and interact with matter and its accompanying electromagnetic fields in different ways. Virtual photons exist everywhere and their effects are observable as the Lamb shift as they interact with the electromagnetic field of electrons surrounding atoms. This activity also underlies zero-point energy, which jostles matter to such an extent it prevents helium at near-absolute zero from freezing at room pressure. Virtual photons are also responsible for the Casimir effect, which squeezes two closely spaced plates together. Virtual photons can also be polarized; this is to say, they have the quantum property of spin-angular momentum, which can couple to the angular momentum of charged particles.In simple terms, all three of the above effects: the Lamb shift, the Casimir force, and the inability of helium to freeze at room pressure due to zero-point energy, arise from the collective activity of virtual photons. More precisely—and ponderously—these three effects are the result of oscillations in the quantum electrodynamic field, resulting in a non-zero QED vacuum (or simply vacuum energy). The QED vacuum is the lowest energy state of the all-pervasive electromagnetic field permeating the Universe; real photons are traveling excitations in this electromagnetic field. Note that the quantum electrodynamic field and the electromagnetic field are essentially the same thing except that the former is the quantum-based view of electromagnetism that accounts for a non-zero vacuum energy. Note also that in discussions of Hawking radiation, the term "zero-point energy" is interchangeable in practice with "vacuum energy" but the former is broader and encompasses other zero-point fields, including the quantum chromodynamic vacuum (QCD), which governs interactions at the quark level.The relativistic mass-energy of real photons (their absolute  energy that, as Hawking wrote, is "relative to infinity") is proportional to their momentum vector times the speed of light per , where…</p>
 is energy,
 is the magnitude of the momentum vector, and
 is the speed of light. Individual virtual photons are different from real ones; they may carry any momentum, or relativistic mass-energy, permitted by the Heisenberg uncertainty principle. Thus, any given pair of virtual photons may possess opposite and unequal momenta. However, across a large population of virtual photon pairs, their net momentum averages to zero and so too does their rest mass-energy and relativistic energy.</p>With regard to measurements in the lab of virtual photon momentum, the labels "positive energy" and "negative energy" are relative classifications established by the direction of their momentum vector, p (and accompanying energy) in relation to an external electromagnetic field (from one or more nearby charged particles). This convention comes from the behavior of real photons, which possess positive energy with respect to electrons; this underlies spectral lines where the electrons surrounding atoms transition from a lower-energy atomic orbital to a higher-energy one after absorbing photons. When an individual virtual photon is exchanged between two particles with like charges (followed soon after by its partner), it is considered to have positive energy when its momentum adds energy to the electromagnetic force between them and they more vigorously repel each other. Note that a virtual photon with a positive-energy momentum direction when it is exchanged between two electrons would be classified as possessing a negative-energy momentum if the exchange was between positrons.In the context of Hawking radiation however, the labels "positive energy" and "negative energy" for virtual photons are in an absolute sense, or "relative to infinity," as Hawking wrote. Virtual photons with negative mass-energies in an absolute sense are generally considered as not physically real. This is because a virtual photon possessing positive momentum and positive mass-energy behaves just like easy-to-study real photons whereas a virtual photon possessing negative momentum and negative mass-energy cannot be isolated in the lab and its distinctive property studied. This inability to isolate a virtual photon possessing negative energy is to be expected since in the wave-based view, it is actually an integral part of an individual oscillation in the quantum electrodynamic field (electromagnetic field) permeating the Universe (see image at right) that humans cannot bifurcate.Black holes have the unique ability to do what cannot be done in the lab: separate virtual photon pairs; Hawking was clear about this in his paper. In Mathur's scientific paper, The fuzzball proposal for black holes: an elementary review (PDF), he endeavored to explain in greater detail the mechanism that allows the quantum information describing what fell into a black hole to be imprinted in Hawking radiation. Mathur wrote that since the radius of curvature near supermassive black holes is larger than both the Planck length and the size of strings, supermassive black holes would seemingly be incapable of violating Hawking’s argument; i.e., such holes would continuously separate virtual photon pairs, creating a problem for quantum theory. Mathur posited that the problem is resolved in the following way: "Bound states" (oscillations in quantum fields like the QED field) grow larger with increasing "degeneracy"; which is to say, spacetime and gravity near event horizons are so agitated that different quantum states begin to share the same energy levels. Essentially, near event horizons where spacetime is close to no longer existing, the quantum property of size smears, enlarges, and overlaps with other quantum properties. This changes the structure of the black hole from what Hawking had imagined to something more like a "string star." A string star does not separate photon pairs the way a traditional black hole does, and thus Hawking’s puzzle is resolved.From the perspective of an outside observer viewing wave-based phenomena, black holes can shear, stretch, and bifurcate the components of a QED oscillation possessing opposite momenta. Hawking radiation arises when the portion of the oscillation possessing negative momentum and negative relativistic mass-energy (the lower bulge of the QED oscillation at right) tunnels through to a black hole. This liberates the positive-energy half of the QED oscillation as a real photon, which becomes exceedingly gravitationally redshifted as it climbs up the extreme gravity well surrounding the black hole and escapes to infinity. The peak-emission wavelength of fully redshifted photons is about ten times the diameter of the event horizon surrounding a non-spinning black hole regardless of its mass; a 6.77  non-spinning black hole with an event horizon diameter of 40.0 kilometers emits Hawking radiation where the most common photons have a wavelength of 403 kilometers.Finally, it is important to bear in mind that gravity and spacetime are so agitated near a black hole that even the mathematics describing Hawking radiation can be viewed in different ways. For instance, instead of negative-energy particles tunneling through the horizon in forward-directed time, they can be thought of, as Hawking wrote in his paper, "as positive-energy particles crossing the horizon on past-directed world-lines." As mentioned earlier, Hawking cautioned that, "It should be emphasized that the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally." Even the basic premiss that Hawking radiation is the product of a stationary person observing a highly accelerating region of spacetime  has its general relativity inverse known as the Unruh effect, which predicts that thermal radiation surrounds an accelerating observer. A helpful YouTube video, "Hawking radiation", by ScienceClic English provides a very visual and detailed explanation of virtual particles, Hawking radiation, and how there are different ways of looking at these phenomena.</ref> The virtual photon possessing negative energy is captured; it travels down through the event horizon via quantum tunneling whereupon it becomes part of the black hole (robbing it of energy and an equivalent amount of mass). Meanwhile, the pair member with positive energy is ejected, carrying away its share of energy from the black hole as blackbody thermal emissions; this is Hawking radiation wherein the ejected photons are no longer virtual and are real. It is important to bear in mind that the above description of the origin of Hawking radiation is highly simplified. Even though Hawking's scientific paper, Particle Creation by Black Holes, was directed to theoretical physicists and delved into arcane phenomena like Killing vector fields, Hawking cautioned that his descriptions of the mechanism responsible for black hole thermal emission "are heuristic only and should not be taken too literally." Note that heuristic teaching means "a teaching method where students learn on their own through discovery and problem-solving in lieu of pure instruction," however, in theoretical physics the verb heuristic can connote "treated in a simpler manner than it really is" whereas the compound noun heuristic approach tends to mean "a simpler or more intuitive way to examine or explain a phenomenon." Nonetheless, Hawking's advisement to his peers to not take his explanations too literally bears witness to the complexities underlying Hawking radiation. His advisement also underscores his remarkable achievement of producing a mathematical formula that relates photon emissions from black holes of any given mass to a blackbody temperature. Within that formula, Hawking linked thermodynamics to a variety of disparate disciplines in physics: quantum mechanics, relativity, Newtonian mechanics, and gravitation, as shown below. The amount of Hawking radiation emitted by black holes, or their luminosity, is inversely proportional to the square of their mass. Such calculations assume that Hawking radiation comprises only photons; that assumption is used throughout this and related articles on Wikipedia. That equation is as follows: 

The term  (luminosity) represents power in watts (an exceedingly small portion of a watt for Hawking radiation), which can be converted to other measures such as mass loss rates. Details on the formula's other terms are beyond the scope of this article and are covered at Bekenstein–Hawking formula. The formula's name honors Jacob Bekenstein (1947–2015), who laid down important foundations to black hole theory that predated Hawking's contributions by several years. In a purely theoretical sense, the fuzzball theory advanced by Mathur and Lunin 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. While Einstein made important contributions to quantum mechanics, he had objections to it. Throughout the remainder of his career, Einstein searched in vain for a unifying theory—a Theory of Everything, so to speak, that explained all aspects of the universe. To this day, there is no widely accepted theory of quantum gravity—a quantum description of gravity—that is in harmony with general relativity, however, both fuzzball theory and other forms of string theory such as M-theory have been advanced as candidates. Testability of the theory 
As no direct experimental evidence supports 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 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. Fuzzball theory cannot be substantiated by observing its predicted subtle effects on Hawking radiation because the radiation itself is, for all practical purposes, undetectable. However, Fuzzball theory may be testable through gravitational-wave astronomy. 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 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, 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 with a temperature of around 23 billionths of one kelvin above absolute zero. 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  of a drop of water (about one-quarter the volume of a common 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; 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* (Fig. 7), 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. Fuzzball theory may however, be testable though gravitational-wave astronomy. Gravitational wave observatories like the Laser Interferometer Gravitational-Wave Observatory (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 gravity waves, a 2015 event known as GW150914, which was a merger between a binary pair of stellar-mass black holes, gravity-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 gravity-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 gravity-wave detectors, such as the proposed Laser Interferometer Space Antenna (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. See also 

 Black hole information paradox
 Black hole thermodynamics
 Cosmic censorship hypothesis
 Degenerate matter
 Ergosphere
 Event horizon
 General relativity
 Gravitational singularity
 Hawking radiation
 Horizon (general relativity) (a list of types)
 M-theory
 Minkowski space
 Neutron star
 Planck star
 Rotating black hole
 Quantum foam
 Quantum gravity
 Spacetime
 Spacetime diagram
 Spaghettification
 Special relativity
 String (physics)
 String theory
 Supermassive black hole
 Superstring theory
 Timeline of black hole physics
 Virtual particle

Notes

References

External links 
 Are Black Holes Fuzzballs? — Space Today Online
 The Fuzzball Fix for a Black Hole Paradox, June 23, 2015 — Quanta Magazine
 Information paradox solved? If so, Black Holes are "Fuzzballs" — 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 and the NIST
 Video lecture series at CERN (four parts approximately an hour each): "The black hole information problem and the fuzzball proposal", Part 1, Part 2, Part 3, Part 4

String theory
Black holes
Hypothetical stars
Stellar black holes