Hawking radiation is

black-body radiation Black-body radiation is the thermal radiation, thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific ...

released outside a

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 ...

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 ...

due to quantum effects according to a model developed 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 ...

in 1974. The radiation was not predicted by previous models which assumed that once

electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...

is inside the event horizon, it cannot escape. Hawking radiation is predicted to be extremely faint and is many orders of magnitude below the current best

telescope A telescope is a device used to observe distant objects by their emission, Absorption (electromagnetic radiation), absorption, or Reflection (physics), reflection of electromagnetic radiation. Originally, it was an optical instrument using len ...

s' detecting ability. Hawking radiation would reduce the

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 ...

and

rotational energy Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the ob ...

of black holes and consequently cause black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. For all except the smallest black holes, this happens extremely slowly. The radiation temperature, called Hawking temperature, is inversely proportional to the black hole's mass, so

micro black hole Micro black holes, also known as mini black holes and quantum mechanical black holes, are hypothetical tiny (<1 )

primordial black hole In cosmology, primordial black holes (PBHs) are hypothetical black holes that formed soon after the Big Bang. In the inflationary era and early radiation-dominated universe, extremely dense pockets of subatomic matter may have been tightly pac ...

s, they will lose mass more rapidly as they shrink, leading to a final cataclysm of high energy radiation alone. Such radiation bursts have not yet been detected.

Background

Modern black holes were first predicted by

Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

's 1915 theory of

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 ...

. Evidence of the astrophysical objects termed

black holes 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 ...

began to mount half a century later, and these objects are of current interest primarily because of their compact size and immense

gravitational attraction In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force be ...

. Early research into black holes was done by individuals such as

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 ...

and John Wheeler, who modeled black holes as having zero entropy. A black hole can form when enough

matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic pa ...

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

is compressed into a volume small enough that 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 ...

is greater than the speed of light. Because nothing can travel that fast, nothing within a certain distance, proportional to the mass of the black hole, can escape beyond that distance. The region beyond which not even light can escape is the

: an observer outside it cannot observe, become aware of, or be affected by events within the event horizon. Andrew Hamilton schwarzchild waterfall

Alternatively, using a set of infalling coordinates in general relativity, one can conceptualize the event horizon as the region beyond which space is infalling faster than the speed of light. (Although nothing can travel ''through'' space faster than light, space itself can infall at any speed.) Once matter is inside the event horizon, all of the matter inside falls inevitably into a

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 ...

, a place of infinite curvature and zero size, leaving behind a warped spacetime devoid of any matter; a classical black hole is pure empty

spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...

, and the simplest (nonrotating and uncharged) is characterized just by its mass and event horizon.

Discovery

In 1971 Soviet scientists

Yakov Zeldovich Yakov Borisovich Zeldovich (, ; 8 March 1914 – 2 December 1987), also known as YaB, was a leading Soviet people, Soviet Physics, physicist of Belarusians, Belarusian origin, who is known for his prolific contributions in physical Physical c ...

and

Alexei Starobinsky Alexei Alexandrovich Starobinsky (; 19 April 1948 – 21 December 2023) was a Soviet and Russian-Jewish theoretical physicist and cosmologist. He was a pioneer of the theory of cosmic inflation, for which he received the 2014 Kavli Prize in ...

proposed that

rotating black hole A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry. All currently known celestial objects, including planets, stars (Sun), galaxies, and black holes, spin about one ...

s ought to create and emit particles, reasoning by analogy with electromagnetic spinning metal spheres. In 1972,

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 ...

developed a theory and reported that the black holes should have an entropy proportional to their surface area. Initially

argued against Bekenstein's theory, viewing black holes as a simple object with no entropy. After meeting Zeldovich in Moscow in 1973, Hawking put these two ideas together using his mixture of quantum field theory and general relativity. In his 1974 paper Hawking showed that in theory, black holes radiate particles as if it were a blackbody. Particles escaping effectively drain energy from the black hole. Due to Bekenstein's contribution to black hole entropy, it is also known as Bekenstein–Hawking radiation. Hawking radiation derives from

vacuum fluctuations In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. ...

. A quantum fluctuation in the electromagnetic field can result in a photon outside of the black hole horizon paired with one on the inside. The horizon allows one to escape in each direction.

Emission process

Hawking radiation is dependent on the

Unruh effect The Unruh effect (also known as the Fulling–Davies–Unruh effect) is a theoretical prediction in quantum field theory that an observer who is uniformly accelerating through empty space will perceive a thermal bath. This means that even in the ...

and the

equivalence principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...

applied to black-hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation.For an accessible discussion of the Unruh effect and Hawking radiation, see: A

Schwarzschild black hole In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...

has a metric :

(\mathrms)^2 = -\left(1 - \frac\right)\,(\mathrmt)^2 + \frac \,(\mathrmr)^2 + r^2\,(\mathrm\Omega)^2.

The black hole is the background spacetime for a quantum field theory. The field theory is defined by a local path integral, so if the boundary conditions at the horizon are determined, the state of the field outside will be specified. To find the appropriate boundary conditions, consider a stationary observer just outside the horizon at position :

r = 2M + \frac.

The local metric to lowest order is :

(\mathrms)^2 = -\left(\frac\right)^2 \,(\mathrmt)^2 + (\mathrm\rho)^2 + (\mathrmX_\perp)^2 = -\rho^2 \,(\mathrm\tau)^2 + (\mathrm\rho)^2 + (\mathrmX_\perp)^2,

which is Rindler in terms of . The metric describes a frame that is accelerating to keep from falling into the black hole. The local acceleration, , diverges as . The horizon is not a special boundary, and objects can fall in. So the local observer should feel accelerated in ordinary Minkowski space by the principle of equivalence. The near-horizon observer must see the field excited at a local temperature :

T = \frac = \frac = \frac,

which is the

. The gravitational redshift is given by the square root of the time component of the metric. So for the field theory state to consistently extend, there must be a thermal background everywhere with the local temperature redshift-matched to the near horizon temperature: :

T(r') = \frac \sqrt\frac = \frac.

The inverse temperature redshifted to at infinity is :

T(\infty) = \frac,

and is the near-horizon position, near , so this is really :

T(\infty) = \frac.

Thus a field theory defined on a black-hole background is in a thermal state whose temperature at infinity is :

T_\text = \frac.

From the black-hole temperature, it is straightforward to calculate the black-hole entropy . The change in entropy when a quantity of heat is added is :

\mathrmS = \frac = 8 \pi M \,\mathrmQ.

The heat energy that enters serves to increase the total mass, so :

\mathrmS = 8 \pi M \,\mathrmM = \mathrm(4 \pi M^2).

So the entropy of a black hole is proportional to its surface area: :

S = 4 \pi M^2 = \frac,

where, since the radius of the black hole is twice its mass, we have that the area A is given by :

A = 4 \pi R^2= 16 \pi M^2.

Assuming that a small black hole has zero entropy, the integration constant is zero. Forming a black hole is the most efficient way to compress mass into a region, and this entropy is also a bound on the information content of any sphere in space time. The form of the result strongly suggests that the physical description of a gravitating theory can be somehow encoded onto a bounding surface.

Black hole evaporation

When particles escape, the black hole loses a small amount of its energy and therefore some of its mass (mass and energy are related by

Einstein's equation In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Albert Einstein in 1915 in th ...

). Consequently, an evaporating black hole will have a finite lifespan. By dimensional analysis, the life span of a black hole can be shown to scale as the cube of its initial mass, and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately 10¹² kg would have evaporated completely by the present day. In 1976, Don Page refined this estimate by calculating the power produced, and the time to evaporation, for a non-rotating, non-charged

of mass . The time for the event horizon or entropy of a black hole to halve is known as the Page time. The calculations are complicated by the fact that a black hole, being of finite size, is not a perfect black body; the

absorption cross section In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department o ...

goes down in a complicated,

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 ...

-dependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon. Page concluded that primordial black holes could survive to the present day only if their initial mass were roughly or larger. Writing in 1976, Page using the understanding of neutrinos at the time erroneously worked on the assumption that neutrinos have no mass and that only two neutrino flavors exist, and therefore his results of black hole lifetimes do not match the modern results which take into account 3 flavors of neutrinos with nonzero masses. A 2008 calculation using the particle content of 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 ...

and the

WMAP The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic mic ...

figure for the age of the universe yielded a mass bound of . Some pre-1998 calculations, using outdated assumptions about neutrinos, were as follows: If black holes evaporate under Hawking radiation, a solar mass black hole will evaporate over 10⁶⁴ years which is vastly longer than the age of the universe.See page 596: table 1 and the "black hole decay" section and previous sentence on that page in A supermassive black hole with a mass of 10¹¹ (100 billion) will evaporate in around . Some monster black holes in the universe are predicted to continue to grow up to perhaps 10¹⁴ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 2 × 10¹⁰⁶ years. Post-1998 science modifies these results slightly; for example, the modern estimate of a solar-mass black hole lifetime is 10⁶⁷ years. The

power Power may refer to: Common meanings * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power, a type of energy * Power (social and political), the ability to influence people or events Math ...

emitted by a black hole in the form of Hawking radiation can be estimated for the simplest case of a nonrotating, non-charged

of mass . Combining the formulas for 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 the black hole, the

Stefan–Boltzmann law The Stefan–Boltzmann law, also known as ''Stefan's law'', describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Lu ...

of blackbody radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

(the black hole's event horizon), several equations can be derived. The Hawking radiation temperature is: :

T_\mathrm = \frac

The Bekenstein–Hawking luminosity of a black hole, under the assumption of pure photon emission (i.e. that no other particles are emitted) and under the assumption that the horizon is the radiating surface is: :

P = \frac

where is the

luminosity Luminosity is an absolute measure of radiated electromagnetic radiation, electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electroma ...

, i.e., the radiated power, is the

reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

, is 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 ...

, is the

gravitational constant The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...

and is the mass of the black hole. It is worth mentioning that the above formula has not yet been derived in the framework of

semiclassical gravity Semiclassical gravity is an approximation to the theory of quantum gravity in which one treats matter and energy fields as being quantum and the gravitational field as being classical. In semiclassical gravity, matter is represented by quantum ...

. The time that the black hole takes to dissipate is: :

t_\mathrm = \frac = \frac = 5120\pi\,t_\left(\frac\right)^ \approx 8.408 \times 10^ \, \mathrm \  \left(  \right)^3 \approx 2.140\times10^\,\text \ \left(\frac\right)^3,

where and are the mass and (Schwarzschild) volume of the black hole, and are Planck mass and Planck time. A black hole of one

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 ...

( = ) takes more than to evaporate—much longer than the current

age of the universe In physical cosmology, the age of the universe is the cosmological time, time elapsed since the Big Bang: 13.79 billion years. Astronomers have two different approaches to determine the age of the universe. One is based on a particle physics ...

at . But for a black hole of , the evaporation time is . This is why some astronomers are searching for signs of exploding primordial black holes. Since the universe contains the

cosmic microwave background radiation 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 ...

, in order for the black hole to dissipate, the black hole must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.7 K. The relationship between mass and temperature for Hawking radiation then implies the mass must be less than 0.8% of the mass of the

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

. This in turn means any black hole that could dissipate cannot be one created by stellar collapse. Only primordial black holes might be created with this little mass. Black hole evaporation has several significant consequences: * Black hole evaporation produces a more consistent view of

black hole thermodynamics In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. As the study of the statistical mechanics of black-body radiation led to the deve ...

by showing how black holes interact thermally with the rest of the universe. * Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of

gamma ray A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...

s. A complete description of this dissolution requires a model 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 ...

, however, as it occurs when the black hole's mass approaches 1

Planck mass 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 ...

, its radius will also approach two

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. * The simplest models of black hole evaporation lead to the

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

. The information content of a black hole appears to be lost when it dissipates, as under these models the Hawking radiation is random (it has no relation to the original information). A number of solutions to this problem have been proposed, including suggestions that Hawking radiation is perturbed to contain the missing information, that the Hawking evaporation leaves some form of remnant particle containing the missing information, and that information is allowed to be lost under these conditions.

Problems and extensions

Trans-Planckian problem

The trans-Planckian problem is the issue that Hawking's original calculation includes

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

particles where the

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

becomes shorter than the

near the black hole's horizon. This is due to the peculiar behavior there, where time stops as measured from far away. A particle emitted from a black hole with a

finite Finite may refer to: * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked for person and/or tense or aspect * "Finite", a song by Sara Gr ...

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

, if traced back to the horizon, must have had an infinite frequency, and therefore a trans-Planckian wavelength. The

and the Hawking effect both talk about field modes in the superficially stationary

that change frequency relative to other coordinates that are regular across the horizon. This is necessarily so, since to stay outside a horizon requires acceleration that constantly

Doppler shift The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The ''Doppler effect'' is named after the physicist Christian Doppler, who described t ...

s the modes. An outgoing

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 ...

of Hawking radiation, if the mode is traced back in time, has a frequency that diverges from that which it has at great distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the black hole. In a maximally extended external

Schwarzschild solution In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...

, that photon's frequency stays regular only if the mode is extended back into the past region where no observer can go, so Hawking used a different black hole solution without a past region, one that forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified: a microscopic point right at the moment that the black hole first formed. The quantum fluctuations at that tiny point, in Hawking's original calculation, contain all the outgoing radiation. The modes that eventually contain the outgoing radiation at long times are redshifted by such a huge amount by their long sojourn next to the event horizon that they start off as modes with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some find Hawking's original calculation unconvincing. The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations. The same effect occurs for regular matter falling onto a

white hole In general relativity, a white hole is a hypothetical region of spacetime and Gravitational singularity, singularity that cannot be entered from the outside, although energy, matter, light and information can escape from it. In this sense, it is ...

solution. Matter that falls on the white hole accumulates on it, but has no future region into which it can go. Tracing the future of this matter, it is compressed onto the final singular endpoint of the white hole evolution, into a trans-Planckian region. The reason for these types of divergences is that modes that end at the horizon from the point of view of outside coordinates are singular in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon. There exist alternative physical pictures that give the Hawking radiation in which the trans-Planckian problem is addressed. The key point is that similar trans-Planckian problems occur when the modes occupied with Unruh radiation are traced back in time.For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation, see: In the Unruh effect, the magnitude of the temperature can be calculated from ordinary Minkowski field theory, and is not controversial.

Large extra dimensions

The formulas from the previous section are applicable only if the laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below the Planck mass (~), they result in impossible lifetimes below the Planck time (~). This is normally seen as an indication that the Planck mass is the lower limit on the mass of a black hole. In a model with

large extra dimensions In particle physics and string theory (M-theory), the Arkani-Hamed, Dimopoulos, Dvali model (ADD), also known as the model with large extra dimensions (LED), is a model framework that attempts to solve the hierarchy problem (''Why is the force of g ...

(10 or 11), the values of Planck constants can be radically different, and the formulas for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole with a radius below the scale of the extra dimensions is given by equation 9 in Cheung (2002) and equations 25 and 26 in Carr (2005). :

\tau \sim \frac \left( \frac \right)^\frac,

where is the low-energy scale, which could be as low as a few TeV, and is the number of large extra dimensions. This formula is now consistent with black holes as light as a few TeV, with lifetimes on the order of the "new Planck time" ~.

In loop quantum gravity

A detailed study of the quantum geometry of a black hole

has been made using

loop quantum gravity Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based direc ...

.001.08833Black Hole evaporation: A Perspective from Loop Quantum Gravity"> Loop-quantization does not reproduce the result for

black hole entropy In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. As the study of the statistical mechanics of black-body radiation led to the developme ...

originally discovered by Bekenstein and Hawking, unless the value of a free parameter is set to cancel out various constants such that the Bekenstein–Hawking entropy formula is reproduced. However, quantum gravitational corrections to the entropy and radiation of black holes have been computed based on the theory. Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking radiation spectrum that would be observable were

X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...

s from Hawking radiation of evaporating primordial black holes to be observed. The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of the Hawking spectrum.

Experimental observation

Astronomical search

In June 2008,

NASA The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States ...

launched the Fermi space telescope, which is searching for the terminal gamma-ray flashes expected from evaporating

s. As of Jan 1st, 2024, none have been detected.

Heavy-ion collider physics

If speculative

large extra dimension In particle physics and string theory (M-theory), the Arkani-Hamed, Dimopoulos, Dvali model (ADD), also known as the model with large extra dimensions (LED), is a model framework that attempts to solve the hierarchy problem (''Why is the force of ...

theories are correct, then

CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...

Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...

may be able to create micro black holes and observe their evaporation. No such micro black hole has been observed at CERN.

Experimental

Under experimentally achievable conditions for gravitational systems, this effect is too small to be observed directly. It was predicted that Hawking radiation could be studied by analogy using sonic black holes, in which sound perturbations are analogous to light in a gravitational black hole and the flow of an approximately

perfect fluid In physics, a perfect fluid or ideal fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure . Real fluids are viscous ("sticky") and contain (and conduct) heat. Perfect fluids are id ...

is analogous to gravity (see ''

Analog models of gravity Analog models of gravity are attempts to model various phenomena of general relativity (e.g., black holes or cosmological geometries) using other physical systems such as waves in a moving fluid and electromagnetic waves in a dielectric medium. The ...

''). Observations of Hawking radiation were reported, in sonic black holes employing

Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low Density, densities is cooled to temperatures very close to absolute zero#Relation with Bose–Einste ...

s. In September 2010 an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiation. However, the results remain unverified and debatable, and its status as a genuine confirmation remains in doubt.

References

External links

Hawking radiation calculator tool

The case for mini black holes
A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders {{DEFAULTSORT:Hawking Radiation Black holes Quantum field theory

Radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: * ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...

Astronomical hypotheses Hypotheses in physics 1974 introductions