Fuzzball (string theory)

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

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]

Physical properties

String theory and composition

Samir D. Mathur of Ohio State University 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.^[6] 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 particles, including the force carriers (e.g., photons and gluons), 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), which holds that strings are both "open" (double-ended entities) and "closed" (looped entities) and that there are 9 + 1 spacetime dimensions wherein five of the six extra spatial dimensions are "compactified".^[7]

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 comprising them. Accordingly, fuzzballs are theorized to be the terminal phase of degenerate matter. 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 of a ubiquitous 6.8 solar mass (M_☉) 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 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 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 particles that form close to their event horizons (see § Information paradox, 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 in‑falling 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 calculated using an entirely different mathematical technique 87 years earlier.^[8]

Since the volume of fuzzballs is a function of the Schwarzschild radius (2953 meters per M_☉ 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 6.8 M_☉ fuzzball would have a mean density of 4.0×10¹⁷ kg/m³. 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 (5.155×10⁹⁶ kg/m³), 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 7 M_☉ 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 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 M_☉. 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 M_☉ (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).^[9]

Neutron star collapse

Black holes (or fuzzballs) are produced in various ways, most of which are exceedingly violent mass-shedding events like supernovas, kilonovas, and hypernovas. 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; this limit is not precisely known, but it is believed to lie between 2.2 M_☉ and 2.9 M_☉. If a neutron star exceeds this mass, neutron degeneracy pressure 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 hadrons in its core (neutrons and perhaps a smattering of protons and mesons) 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.

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 and later popularized by

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