Fuzzballs are hypothetical objects in superstring theory, intended to provide a fully quantum description of the black holes predicted by general relativity.

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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 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 familiar dimensions of space as well as in extra dimensions.^[1] Fuzzballs provide resolutions to two major open problems in black hole physics. First, they avoid the gravitational singularity 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, such as superstring theory, are expected to explain its true nature.^[2] 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. This would violate a fundamental law of quantum mechanics requiring that quantum information be conserved.^[1][3]

As no direct experimental evidence supports either string theory in general or fuzzballs in particular, both are products purely of calculations and theoretical research.^{[4][better source needed]} However, the existence of fuzzballs may be testable through gravitational-wave astronomy.^[5]

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 and later popularized by Stephen Hawking. 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.

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 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, which states that black holes can reveal nothing about themselves to outside observers except their mass, angular momentum, and electric charge, whereby the latter two could theoretically be revealed through a phenomenon known as superradiance.^[10]

Stephen Hawking showed that quantum effects will make black holes appear to be blackbody radiators with effective temperatures inversely proportional to the mass of a black hole. This radiation, now called Hawking radiation, 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.^[1]

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—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.^[1][11]

As no direct experimental evidence supports either string theory or fuzzball theory, both are products purely of calculations and theoretical research.^[4] However, theories must be experimentally testable if there is to be a possibility of ascertaining their validity.^[12] 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. 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.^[13] However, fuzzball theory may be testable through gravitational-wave astronomy.^[5]

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 predicts that for each known quanta (particle) in the Standard Model, a superpartner particle exists that differs by spin 1⁄2. This means that for every boson (massless particles in the Standard Model with integer spins like 0, 1, and 2), there is a supersymmetric-spin fermion-like particle known as a gaugino that has a half-odd-integer spin (e.g., 1⁄2 and 3⁄2) and possesses a rest mass. Examining this spin-1⁄2 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 carriers.^[14] 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 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 1⁄2. Conversely, the electron (spin 1⁄2) 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 and the muon's anomalous magnetic moment (it should be precisely equal to 2 and is instead about 2.00233184, suggesting hidden interactions); particle physicists have accordingly been searching for these superpartners.^[15][16] 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.^[17] 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.^[14] Though many searches using particle colliders have ruled out certain mass ranges for supersymmetric particles, the hunt continues.^[18]

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.^[13] 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 4.9 M_☉ black hole would require 10⁵⁹ times the current age of the Universe to vanish. Moreover, a top-of-the-list 106 billion M_☉ supermassive black hole would require ten million-trillion-trillion times longer still to evaporate: 10⁹⁰ times the age of the Universe.^[9]

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, 2.7 M_☉ 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 1.2×10⁻²⁹ watt (12 billion-billion-billionths of one milliwatt).^[9] Such an infinitesimal transmitted power is to one watt as ¹⁄₃₀₀₀th 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; Hawking radiation comprises individual photon quanta, so such a weak signal means a 2.7 M_☉ 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.^[9]

However, fuzzball theory may be testable through 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.^[19] 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.^[5] 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.^[20]