Citizendia

In physics, Hawking radiation (also known as Bekenstein-Hawking radiation) is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. In Physics, a black body is an object that absorbs all light that falls on it A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons It is named after the physicist Stephen Hawking who provided the theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein who predicted that black holes should have a finite, non-zero temperature and entropy. Stephen William Hawking CH, CBE, FRS, FRSA (born 8 January 1942 is a British theoretical physicist. A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning Jacob David Bekenstein (born May 1, 1947) is a Physicist who has contributed to the foundation of Black hole thermodynamics and to other aspects Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Hawking's work followed his visit to Moscow in 1973 where Soviet scientists Yakov Zeldovich and Alexander Starobinsky showed him that according to the quantum mechanical uncertainty principle rotating black holes should create and emit particles. Moscow (Москва́ romanised: Moskvá, IPA: see also other names) is the Capital and the largest city of Yakov Borisovich Zel'dovich (Яков Борисович Зельдович ( March 8, 1914 &ndash December 2, 1987) was a prolific Soviet [1]

Because Hawking radiation allows black holes to lose mass, black holes which lose more matter than they gain through other means are expected to evaporate, shrink, and ultimately vanish. Smaller micro black holes (MBHs) are currently predicted by theory to be larger net emitters of radiation than larger black holes, and to shrink and evaporate faster. Micro black holes, are the tiny hypothetical Black holes also called quantum mechanical black holes or mini black holes, for which quantum mechanical

Hawking's analysis became the first convincing insight into a possible theory of quantum gravity. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature However, the existence of Hawking radiation has never been observed, nor are there currently viable experimental tests which would allow it to be observed. Hence there is still some theoretical dispute over whether Hawking radiation actually exists. However, the GLAST satellite to be launched by NASA in Spring, 2008 will be able to search for evaporating primordial black holes. In speculative large extra dimension theories, CERN's Large Hadron Collider may be able to create micro black holes and observe their evaporation. In Particle physics, the ADD model, also known as the model with large extra dimensions, is an alternative scenario to explain the weakness of Gravity relative [2][3][4]

Ground based observatories, such as the Pierre Auger, might also be capable of detecting evaporating MBHs that would form in the upper atmosphere by the impact of high-speed protons, also known as cosmic rays. Pierre Auger Observatory is an international Cosmic ray observatory designed to detect ultra high energy cosmic rays -- Ultra-high-energy particles These are sub-atomic The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive For the 1962 Bruce Conner film see Cosmic Ray (film Cosmic rays are energetic particles originating from space that impinge on Recent results[5] from the Pierre Auger now suggest that the highest energy protons (with energies of 1020 eV or higher) originate from nearby active galactic nuclei (AGN) where they are accelerated and travel to earth for hundreds of millions of years at nearly the speed of light, and upon impact might create MBHs, allowing for observation of their evaporation. An active galactic nucleus ( AGN) is a compact region at the centre of a Galaxy which has a much higher than normal luminosity over some or all of the Electromagnetic

Contents

Overview

Black holes are sites of immense gravitational attraction into which surrounding matter is drawn by gravitational forces. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Gravitation is a natural Phenomenon by which objects with Mass attract one another Matter is commonly defined as being anything that has mass and that takes up space. Classically, the gravitation is so powerful that nothing, not even radiation can escape from the black hole. Radiation, as in Physics, is Energy in the form of waves or moving Subatomic particles emitted by an atom or other body as it changes from a higher energy It is yet unknown how gravity can be incorporated into quantum mechanics, but nevertheless far from the black hole the gravitational effects can be weak enough that calculations can be reliably performed in the framework of quantum field theory in curved spacetime. Gravitation is a natural Phenomenon by which objects with Mass attract one another Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Quantum field theory in curved spacetime is an extension of standard Quantum field theory to curved spacetime. Hawking showed that quantum effects allow black holes to emit exact black body radiation, which is the average thermal radiation emitted by an idealized thermal source known as a black body. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e The Electromagnetic radiation emitted by a Black body. You may also be looking for Incandescence, the radiation from a body In Physics, a black body is an object that absorbs all light that falls on it The radiation is as if it is emitted by a black body with a temperature that is inversely proportional to the black hole's mass. Radiation, as in Physics, is Energy in the form of waves or moving Subatomic particles emitted by an atom or other body as it changes from a higher energy In Physics, a black body is an object that absorbs all light that falls on it Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature This article is about proportionality the mathematical relation A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object

Physical insight on the process may be gained by imagining that particle-antiparticle radiation is emitted from just beyond the event horizon. In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made to most kinds of particles, there is an associated antiparticle with the same Mass and opposite Electric charge. In General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles. In Physics, a virtual particle is a particle that exists for a limited time and space introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty

A slightly more precise, but still much simplified view of the process is that vacuum fluctuations cause a particle-antiparticle pair to appear close to the event horizon of a black hole. In Physics, a virtual particle is a particle that exists for a limited time and space introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty In General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot One of the pair falls into the black hole whilst the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός By this process the black hole loses mass, and to an outside observer it would appear that the black hole has just emitted a particle. In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made In reality, the process is a quantum tunneling effect, whereby particle-antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon. In Quantum mechanics, quantum tunnelling is a nanoscopic phenomenon in which a particle violates the principles of Classical mechanics by penetrating a

An important difference between the black hole radiation as computed by Hawking and a thermal radiation emitted from a black body is that the latter is statistical in nature, and only its average satisfies what is known as Planck's law of black body radiation, while the former satisfies this law exactly. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Radiation, as in Physics, is Energy in the form of waves or moving Subatomic particles emitted by an atom or other body as it changes from a higher energy Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. In Physics, a black body is an object that absorbs all light that falls on it For a general introduction see Black body. In Physics, Planck's law describes the spectral radiance of Electromagnetic radiation Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum and charge of the black hole. Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. Information as a concept has a diversity of meanings from everyday usage to technical settings Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position In Physics, a charge may refer to one of many different quantities such as the Electric charge in Electromagnetism or the Color charge in This leads to the black hole information paradox. The black hole information paradox results from the combination of Quantum mechanics and General relativity.

However, according to the conjectured gauge-gravity duality (also known as the AdS/CFT correspondence), black holes in certain cases (and perhaps in general) are equivalent to solutions of quantum field theory at a non-zero temperature. String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings For the relation of the AdS/CFT correspondence to the general context of string theory see String theory. In quantum field theory (QFT the forces between particles are mediated by other particles Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature This means that no information loss is expected in black holes (since no such loss exists in the quantum field theory), and the radiation emitted by a black hole is probably a usual thermal radiation. In quantum field theory (QFT the forces between particles are mediated by other particles If this is correct, then Hawking's original computation should be corrected, though it is not known how (see below). Hawking radiation (also known as Bekenstein-Hawking radiation) is a Thermal radiation with a black body spectrum predicted to be emitted by Black holes

An example

A black hole of one solar mass has a temperature of only 60 nanokelvin; in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. A black hole of 4. 5 × 1022 kg (about the mass of the Moon) would be in equilibrium at 2. 7 kelvins, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb, and thereby lose mass. A primordial black hole is a hypothetical type of Black hole that is formed not by the Gravitational collapse of a star but by the extreme density of matter present

Trans-Planckian problem

The trans-Planckian problem is the observation that Hawking's original calculation requires talking about quantum particles in which the wavelength becomes shorter than the Planck length near the black hole horizon. In black hole physics and inflationary cosmology, the trans-Planckian problem refers to the appearance of quantities beyond the Planck scale, which In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. The Planck length, denoted by \scriptstyle\ell_P \, is the unit of Length approximately 1 The horizon ( Ancient Greek ὁ ὁρίζων, /ho horídzôn/ from ὁρίζειν, "to limit" is the apparent line that separates It is due to the peculiar behavior near a gravitational horizon where time stops as measured from far away. A particle emitted from a black hole with a finite frequency, if traced back to the horizon, must have had an infinite frequency there and a trans-Planckian wavelength. Frequency is a measure of the number of occurrences of a repeating event per unit Time. Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness

The Unruh effect and the Hawking effect both talk about field modes in the superficially stationary space-time that change frequency relative to other coordinates which are regular across the horizon. The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS This is necessarily so, since to stay outside a horizon requires acceleration which constantly Doppler shifts the modes. The Doppler effect (or Doppler shift) named after Christian Doppler, is the change in Frequency and Wavelength of a Wave for

An outgoing Hawking radiated photon, if the mode is traced back in time, has a frequency which 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 Physics, the photon is the Elementary particle responsible for electromagnetic phenomena In a maximally extended external Schwarzschild solution, that photon's frequency only stays regular if the mode is extended back into the past region where no observer can go. That region doesn't seem to be observable and is physically suspect, so Hawking used a black hole solution without a past region which forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified – it is 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. [6][7][8][9][10][11]

The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations. [12][13] The same effect occurs for regular matter falling onto a white hole solution. In Astrophysics, a white hole is the theoretical time reversal of a Black hole. Matter which 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 which 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 which 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. The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe [14] In the Unruh effect, the magnitude of the temperature can be calculated from ordinary Minkowski field theory, and is not controversial. Hermann Minkowski ( June 22 1864 – January 12 1909) was a Russian born German Mathematician, of Jewish

Emission process

Hawking radiation is required by the Unruh effect and the equivalence principle applied to black hole horizons. The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe The equivalence principle A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. In General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot An accelerating observer sees a thermal bath of particles which 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. [14]

A Schwarzschild black hole has a metric

ds^2 = -\left(1-{2M\over r}\right)dt^2 + {1\over 1-{2M\over r}} dr^2 + r^2 d\Omega^2.\,

The black hole is the background spacetime for a quantum field theory. In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside

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 + u2 / 2M. The local metric to lowest order is:

ds^2 = - {u^2\over 4M^2} dt^2 + 4 du^2 + dX_\perp^2 = - \rho^2 d\tau^2 + d\rho^2 + dX_\perp^2,\,

which is Rindler in terms of τ = t / 4M and ρ = 2u The metric describes a frame which is accelerating to keep from falling into the black hole. The local acceleration diverges as u\rightarrow 0.

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 inverse temperature

\beta(u)=2\pi \rho = (4\pi) u = 4\pi \sqrt{2M(r-2M)}\,,

the Unruh effect. The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe

The gravitational redshift is 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:

\beta(r') = 4\pi \sqrt{2M(r-2M)} \sqrt{1-{2M\over r'} \over 1-{2M\over r}} \,

The inverse temperature redshifted to r' at infinity is

\beta(\infty) = (4\pi)\sqrt{2Mr} \,

and r is the near-horizon position, near 2M, so this is really:

\beta = 8\pi M\,

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

T_H = {1\over 8\pi M}\,

Which can be expressed more cleanly in terms of the surface gravity of the black hole, the parameter that determines the acceleration of a near-horizon observer. The surface gravity, g, of an astronomical or other object is the Gravitational acceleration experienced at its surface

T_H = \frac{\kappa}{2 \pi}\,,

in natural units with G, c, \hbar and k equal to 1, and where κ is the surface gravity of the horizon. In Physics, natural units are Physical units of Measurement defined in terms of universal Physical constants, such that some chosen physical The surface gravity, g, of an astronomical or other object is the Gravitational acceleration experienced at its surface So a black hole can only be in equilibrium with a gas of radiation at a finite temperature. Since radiation incident on the black hole is absorbed, the black hole must emit an equal amount to maintain detailed balance. In Mathematics and Statistical mechanics, a Markov process is said to show detailed balance if the transition rates between each pair of states i The black hole acts as a perfect blackbody radiating at this temperature. The Electromagnetic radiation emitted by a Black body. You may also be looking for Incandescence, the radiation from a body

In engineering units, the radiation from a Schwarzschild black hole is black-body radiation with temperature:

T={\hbar\,c^3\over8\pi G M k}\,

where \hbar is the reduced Planck constant, c is the speed of light, k is the Boltzmann constant, G is the gravitational constant, and M is the mass of the black hole. In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside The Electromagnetic radiation emitted by a Black body. You may also be looking for Incandescence, the radiation from a body The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object

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

dS = {dQ\over T} = 8\pi M dQ\,

the heat energy that enters serves increases the total mass:

dS = 8\pi M dM = d(4\pi M^2)\,

The radius of a black hole is twice its mass in natural units, so the entropy of a black hole is proportional to its surface area:

S= \pi R^2 = {A\over 4}\,

Assuming that a small black hole has zero entropy, the integration constant is zero. In Physics, natural units are Physical units of Measurement defined in terms of universal Physical constants, such that some chosen physical 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. Holography (from the Greek, ὅλος - hólos whole + γραφή - grafē writing drawing is a technique that allows the

Black hole evaporation

When particles escape, the black hole loses a small amount of its energy and therefore of its mass (mass and energy are related by Einstein's equation E = mc²). Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial In Physics, mass–energy equivalence is the concept that for particles slower than light any Mass has an associated Energy and vice versa.

The power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild black hole of mass M. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside Combining the formulae for the Schwarzschild radius of the black hole, the Stefan-Boltzmann law of black-body radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a sphere (the black hole's event horizon) we get:

P={\hbar\,c^6\over15360\,\pi\,G^2M^2}

where P is the energy outflow, \hbar is the reduced Planck constant, c is the speed of light, and G is the gravitational constant. The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a characteristic Radius associated with every Mass. The Stefan–Boltzmann law, also known as Stefan's law, states that the total Energy radiated per unit surface Area of a Black body in unit "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe In General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass It is worth mentioning that the above formula has not yet been derived in the framework of semiclassical gravity. Semiclassical gravity is the approximation to the theory of Quantum gravity in which one treats Matter fields as being quantum and the gravitational field

The power in the Hawking radiation from a solar mass black hole turns out to be a minuscule 10−28 watts. The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. It is indeed an extremely good approximation to call such an object 'black'.

Under the assumption of an otherwise empty universe, so that no matter or cosmic microwave background radiation falls into the black hole, it is possible to calculate how long it would take for the black hole to evaporate. Matter is commonly defined as being anything that has mass and that takes up space. The black hole's mass is now a function M(t) of time t. The time that the black hole takes to evaporate is:

t_{\operatorname{ev}}={5120\,\pi\,G^2M_0^{\,3}\over\hbar\,c^4}

For a black hole of one solar mass (about 2 × 1030 kg), we get an evaporation time of 1067 years—much longer than the current age of the universe. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. But for a black hole of 1011 kg, the evaporation time is about 3 billion years. This is why some astronomers are searching for signs of exploding primordial black holes. A primordial black hole is a hypothetical type of Black hole that is formed not by the Gravitational collapse of a star but by the extreme density of matter present

However, since the universe contains the cosmic microwave background radiation, in order for the black hole to evaporate it must have a temperature greater than that of the present-day black-body radiation of the universe of 2. 7 K = 2. 3×10−4 eV. This implies that M must be less than 0. 8% of the mass of the Earth. [15]

In common units,

P = 3.563\,45 \times 10^{32} \left[\frac{\mathrm{kg}}{M}\right]^2 \mathrm{W}
t_\mathrm{ev} = 8.407\,16 \times 10^{-17} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s}\ \ \approx\ 2.66 \times 10^{-24} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{yr}
M_0 = 2.282\,71 \times 10^5 \left[\frac{t_\mathrm{ev}}{\mathrm{s}}\right]^{1/3} \mathrm{kg} \ \ \approx\ 7.2 \times 10^7 \left[\frac{t_\mathrm{ev}}{\mathrm{yr}}\right]^{1/3} \mathrm{kg}

So, for instance, a 1 second-lived black hole has a mass of 2. 28 × 105 kg, equivalent to an energy of 2. 05 × 1022 J that could be released by 5 × 106 megatons of TNT. The initial power is 6. 84 × 1021 W.

Black hole evaporation has several significant consequences:

Hawking radiation and large extra dimensions

Formulas from the previous section are only applicable if laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below Planck mass (~10−5 g), they result in unphysical lifetimes below Planck time (~10−43 s). This is normally seen as an indication that Planck mass is the lower limit on the mass of a black hole.

In the model with large extra dimensions, values of Planck constants can be radically different, and formulas for Hawking radiation have to be modified as well. In Particle physics, the ADD model, also known as the model with large extra dimensions, is an alternative scenario to explain the weakness of Gravity relative In particular, the lifetime of a micro black hole (with radius below the scale of extra dimensions) is given by

\tau \sim {1 \over M_*} \Bigl( {M_{BH} \over M_*} \Bigr) ^{(n+3)/(n+1)}

where M * is the low energy scale (which could be as low as a few TeV), and n 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 "new Planck time" ~10−26 s.

Deviation from Hawking radiation in loop quantum gravity

A detailed study of the quantum geometry of a black hole horizon has been made using Loop quantum gravity. Loop quantum gravity (LQG, also known as loop gravity and Quantum geometry, is a proposed quantum theory of Spacetime which attempts to reconcile the theories Loop-quantization reproduces the result for black hole entropy originally discovered by Bekenstein and Hawking. 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 Jacob David Bekenstein (born May 1, 1947) is a Physicist who has contributed to the foundation of Black hole thermodynamics and to other aspects Further, it led to the computation of quantum gravity corrections to the entropy and radiation of black holes.

Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking spectrum that would be observable were x-rays from Hawking radiation of evaporating primordial black holes to be observed. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. A primordial black hole is a hypothetical type of Black hole that is formed not by the Gravitational collapse of a star but by the extreme density of matter present The deviation is such that the Hawking radiation is expected to be centered at a set of discrete and unblended energies.

Experimental observation of the Hawking radiation

Under experimentally achievable conditions for gravitational systems this effect is too small to be observed. Recent work[16] shows that if one takes an accelerated observer to be an electron circularly orbiting in a constant external magnetic field, then the experimentally verified Sokolov-Ternov effect coincides with the Unruh effect, which is in close connection with the Hawking radiation. The Sokolov-Ternov effect is the effect of self-polarization of relativistic electrons or positrons moving at high energy in a magnetic field The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe

See also

References

Notes

  1. ^ A Brief History of Time, Stephen Hawking, Bantam Books, 1988.
  2. ^ CERN courier - The case for mini black holes. Nov 2004
  3. ^ American Institute of Physics Bulletin of Physics News, Number 558, September 26, 2001, by Phillip F. Schewe, Ben Stein, and James Riordon
  4. ^ Dimopoulos, S. and Landsberg, G. Black Holes at the Large Hadron Collider. Phys. Rev. Lett. 87 (2001).
  5. ^ "Scientists of the Pierre Auger Collaboration announced today (8 Nov. 2007) that Active Galactic Nuclei are the most likely candidate for the source of the highest-energy cosmic rays that hit Earth. Using the Pierre Auger Observatory in Argentina, the largest cosmic-ray observatory in the world, a team of scientists from 17 countries found that the sources of the highest-energy particles are not distributed uniformly across the sky. Instead, the Auger results link the origins of these mysterious particles to the locations of nearby galaxies that have active nuclei in their centers. The results appear in the Nov. 9 issue of the journal Science. "
  6. ^ Adam D. Helfer: General Relativity and Quantum Cosmology
  7. ^ G. 't Hooft, Nuclear Phys B256, 727 (1985)
  8. ^ T. Jacobson, Phys Review D 44 1731 (1991)
  9. ^ http://www.fys.ruu.nl/~wwwthe/lectures/itfuu-0196.ps (p. 46)
  10. ^ R. Brout, S. Massar, R. Parentani, Ph. Spindel, Hawking radiation without trans-Planckian frequencies, Phys. Rev. D 52, 4559 - 4568 (1995)
  11. ^ Helfer, Adam D. Trans-Planckian Modes, Back-Reaction, and the Hawking Process, http://arxiv.org/abs/gr-qc/0008016
  12. ^ Analogue Gravity
  13. ^ http://www.fys.ruu.nl/~wwwthe/lectures/itfuu-0196.ps (p. 46)
  14. ^ a b For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation see Bryce de Witt's chapter Quantum gravity: the new synthesis pg c. The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe Bryce Seligman DeWitt ( January 8, 1923 &ndash September 23, 2004) was a Theoretical physicist best known for formulating Canonical 696 in General Relativity: An Einstein Centenary eds S Hawking and W Israel, ISBN 0521299284
  15. ^ http://arxiv.org/abs/astro-ph/9911309
  16. ^ Emil T Akhmedov, Douglas Singleton On the physical meaning of the Unruh effect

External links

Dictionary

Hawking radiation

-noun

  1. The radiation presumed to be given off by a black hole by quantum mechanical processes.
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