Micro black hole
micro black hole, micro black holesMicro black holes, also called quantum mechanical black holes or mini black holes, are hypothetical tiny black holes, for which quantum mechanical effects play an important role[1] The concept that black holes may exist that are smaller than stellar mass was introduced in 1971 by Stephen Hawking[2]
It is possible that such quantum primordial black holes were created in the highdensity environment of the early Universe or big bang, or possibly through subsequent phase transitions They might be observed by astrophysicists through the particles they are expected to emit by Hawking radiation
Some hypotheses involving additional space dimensions predict that micro black holes could be formed at energies as low as the TeV range, which are available in particle accelerators such as the Large Hadron Collider Popular concerns have then been raised over endoftheworld scenarios see Safety of particle collisions at the Large Hadron Collider However, such quantum black holes would instantly evaporate, either totally or leaving only a very weakly interacting residue[citation needed] Beside the theoretical arguments, the cosmic rays hitting the Earth do not produce any damage, although they reach center of mass energies in the range of hundreds of TeV
Contents
 1 Minimum mass of a black hole
 2 Stability
 21 Hawking radiation
 22 Conjectures for the final state
 3 Primordial black holes
 31 Formation in the early Universe
 32 Expected observable effects
 4 Manmade micro black holes
 41 Feasibility of production
 42 Safety arguments
 43 As a power source
 5 Black holes in quantum theories of gravity
 6 See also
 7 Notes
 8 References
 9 Bibliography
 10 External links
Minimum mass of a black hole
In principle, a black hole can have any mass equal to or above the Planck mass about 6992220000000000000♠22×10−8 kg or 22 micrograms[2] To make a black hole, one must concentrate mass or energy sufficiently that the escape velocity from the region in which it is concentrated exceeds the speed of light This condition gives the Schwarzschild radius, R = 2GM/c2, where G is the gravitational constant, c is the speed of light, and M the mass of the black hole On the other hand, the Compton wavelength, λ = h/Mc, where h is the Planck constant, represents a limit on the minimum size of the region in which a mass M at rest can be localized For sufficiently small M, the reduced Compton wavelength λ = ħ/Mc, where ħ is the reduced Planck constant exceeds half the Schwarzschild radius, and no black hole description exists This smallest mass for a black hole is thus approximately the Planck mass
Some extensions of present physics posit the existence of extra dimensions of space In higherdimensional spacetime, the strength of gravity increases more rapidly with decreasing distance than in three dimensions With certain special configurations of the extra dimensions, this effect can lower the Planck scale to the TeV range Examples of such extensions include large extra dimensions, special cases of the Randall–Sundrum model, and string theory configurations like the GKP solutions In such scenarios, black hole production could possibly be an important and observable effect at the Large Hadron Collider LHC[1][3][4][5][6] It would also be a common natural phenomenon induced by the cosmic rays
All this assumes that the theory of general relativity remains valid at these small distances If it does not, then other, presently unknown, effects will limit the minimum size of a black hole Elementary particles are equipped with a quantummechanical, intrinsic angular momentum spin The correct conservation law for the total orbital plus spin angular momentum of matter in curved spacetime requires that spacetime is equipped with torsion The simplest and most natural theory of gravity with torsion is the Einstein–Cartan theory[7][8] Torsion modifies the Dirac equation in the presence of the gravitational field and causes fermion particles to be spatially extended[9]
The spatial extension of fermions limits the minimum mass of a black hole to be on the order of 7016100000000000000♠1016 kg, showing that micro black holes may not exist The energy necessary to produce such a black hole is 39 orders of magnitude greater than the energies available at the Large Hadron Collider, indicating that the LHC cannot produce mini black holes But if black holes are produced, then the theory of general relativity is proven wrong and does not exist at these small distances The rules of general relativity would be broken, as is consistent with theories of how matter, space, and time break down around the event horizon of a black hole This would prove the spatial extensions of the fermion limits to be incorrect as well The fermion limits assume a minimum mass needed to sustain a black hole, as opposed to the opposite, the minimum mass needed to start a black hole, which in theory is achievable in the LHC[10]
Stability
Hawking radiation
Main article: Hawking radiationIn 1974, Stephen Hawking argued that, due to quantum effects, black holes "evaporate" by a process now referred to as Hawking radiation in which elementary particles such as photons, electrons, quarks, gluons are emitted[2] His calculations showed that the smaller the size of the black hole, the faster the evaporation rate, resulting in a sudden burst of particles as the micro black hole suddenly explodes
Any primordial black hole of sufficiently low mass will evaporate to near the Planck mass within the lifetime of the Universe In this process, these small black holes radiate away matter A rough picture of this is that pairs of virtual particles emerge from the vacuum near the event horizon, with one member of a pair being captured, and the other escaping the vicinity of the black hole The net result is the black hole loses mass due to conservation of energy According to the formulae of black hole thermodynamics, the more the black hole loses mass, the hotter it becomes, and the faster it evaporates, until it approaches the Planck mass At this stage, a black hole would have a Hawking temperature of TP/8π 7032560000000000000♠56×1032 K, which means an emitted Hawking particle would have an energy comparable to the mass of the black hole Thus, a thermodynamic description breaks down Such a micro black hole would also have an entropy of only 4π nats, approximately the minimum possible value At this point then, the object can no longer be described as a classical black hole, and Hawking's calculations also break down
While Hawking radiation is sometimes questioned,[11] Leonard Susskind summarizes an expert perspective in his book The Black Hole War: "Every so often, a physics paper will appear claiming that black holes don't evaporate Such papers quickly disappear into the infinite junk heap of fringe ideas"[12]
Conjectures for the final state
Conjectures for the final fate of the black hole include total evaporation and production of a Planckmasssized black hole remnant Such Planckmass black holes may in effect be stable objects if the quantized gaps between their allowed energy levels bar them from emitting Hawking particles or absorbing energy gravitationally like a classical black hole In such case, they would be weakly interacting massive particles; this could explain dark matter[13]
Primordial black holes
Main article: Primordial black holeFormation in the early Universe
Production of a black hole requires concentration of mass or energy within the corresponding Schwarzschild radius It is hypothesized by Zel'dovich and Novikov first and independently by Hawking that, shortly after the Big Bang, the Universe was dense enough for any given region of space to fit within its own Schwarzschild radius Even so, at that time, the Universe was not able to collapse into a singularity due to its uniform mass distribution and rapid growth This, however, does not fully exclude the possibility that black holes of various sizes may have emerged locally A black hole formed in this way is called a primordial black hole and is the most widely accepted hypothesis for the possible creation of micro black holes Computer simulations suggest that the probability of formation of a primordial black hole is inversely proportional to its mass Thus, the most likely outcome would be micro black holes[citation needed]
Expected observable effects
A primordial black hole with an initial mass of around 7012100000000000000♠1012 kg would be completing its evaporation today; a less massive primordial black hole would have already evaporated[1] In optimistic circumstances, the Fermi Gammaray Space Telescope satellite, launched in June 2008, might detect experimental evidence for evaporation of nearby black holes by observing gamma ray bursts[14][15][16] It is unlikely that a collision between a microscopic black hole and an object such as a star or a planet would be noticeable The small radius and high density of the black hole would allow it to pass straight through any object consisting of normal atoms, interacting with only few of its atoms while doing so It has, however, been suggested that a small black hole of sufficient mass passing through the Earth would produce a detectable acoustic or seismic signal[17][18][19][a]
Manmade micro black holes
Feasibility of production
In familiar threedimensional gravity, the minimum energy of a microscopic black hole is 7009160217648700000♠1019 GeV, which would have to be condensed into a region on the order of the Planck length This is far beyond the limits of any current technology It is estimated[citation needed] that to collide two particles to within a distance of a Planck length with currently achievable magnetic field strengths would require a ring accelerator about 1,000 light years in diameter to keep the particles on track Stephen Hawking also said in chapter 6 of his A Brief History of Time that physicist John Archibald Wheeler once calculated that a very powerful hydrogen bomb using all the deuterium in all the water on Earth could also generate such a black hole, but Hawking does not provide this calculation or any reference to it to support this assertion
However, in some scenarios involving extra dimensions of space, the Planck mass can be as low as the TeV range The Large Hadron Collider LHC has a design energy of 6994224304708180000♠14 TeV for proton–proton collisions and 1,150 TeV for Pb–Pb collisions It was argued in 2001 that, in these circumstances, black hole production could be an important and observable effect at the LHC[3][4][5][6][20] or future higherenergy colliders Such quantum black holes should decay emitting sprays of particles that could be seen by detectors at these facilities[3][4] A paper by Choptuik and Pretorius, published in 2010 in Physical Review Letters, presented a computergenerated proof that micro black holes must form from two colliding particles with sufficient energy, which might be allowable at the energies of the LHC if additional dimensions are present other than the customary four three spatial, one temporal[21][22]
Safety arguments
Main article: Safety of highenergy particle collision experimentsHawking's calculation[2] and more general quantum mechanical arguments predict that micro black holes evaporate almost instantaneously Additional safety arguments beyond those based on Hawking radiation were given in the paper,[23][24] which showed that in hypothetical scenarios with stable black holes that could damage Earth, such black holes would have been produced by cosmic rays and would have already destroyed known astronomical objects such as the Earth, Sun, neutron stars, or white dwarfs
As a power source
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If a way to create artificial micro black holes were discovered, they could provide an abundant energy source by absorbing and converting their Hawking radiation The process may occur with a smaller mass black hole evaporating as a gamma ray burst immediately after creation It may also occur in a zerogravity environment, with a largermass black hole, that may emit radiation for years before becoming unstable and needing replacement, such as in a black hole starship
This was explored in Arthur C Clarke's books such as Imperial Earth and in fact recent calculations[which] suggest that mini BHs may be stable if they are larger than a critical size as long as they are fed a continuous stream of energy tuned to the diameter of the event horizon Some[who] have suggested using a particle acceleratorlike device to achieve this It has also been theorized[by whom] that very small black holes in nature may be detected, captured and used by an advanced civilization as a power source whose containment failure might be seen as an atypical gravitational wave event, we may even have detected microblack holes indirectly as anomalous clock variations on GPS satellites, FRBs and coincidental seismic signals[citation needed]
In 2009 scientists Qiang Cheng and Tie Jun Cui from Southeast University in Nanjing, China created an artificial version of a black hole using concentric circles of metamaterial which trapped radiation from all directions MITtechnologyreview/ This raises the question whether human interest in and understanding of black holes could support attempts to improve the efficiency of light harvesting for green energy
Black holes in quantum theories of gravity
It is possible, in some theories of quantum gravity, to calculate the quantum corrections to ordinary, classical black holes Contrarily to conventional black holes, which are solutions of gravitational field equations of the general theory of relativity, quantum gravity black holes incorporate quantum gravity effects in the vicinity of the origin, where classically a curvature singularity occurs According to the theory employed to model quantum gravity effects, there are different kinds of quantum gravity black holes, namely loop quantum black holes, noncommutative black holes, asymptotically safe black holes In these approaches, black holes are singularityfree
Virtual micro black holes have been proposed by Stephen Hawking in 1995,[25] and by Fabio Scardigli in 1999 as part of a Grand Unified Theory which could be a quantum gravity candidate[26][27]
See also
 Black holes in fiction
 Planck particle
 Holeum
 Kugelblitz astrophysics
 Black hole starship
 Black hole electron
Notes
 ^ The Schwarzschild radius of a 7012100000000000000♠1012 kg black hole is approximately 6987148000000000000♠148 fm 6987148000000000000♠148×10−13 m, which is much smaller than an atom but larger than an atomic nucleus
References
 ^ a b c Carr, B J; Giddings, S B 2005 "Quantum black holes" Scientific American 292 5: 30
 ^ a b c d Hawking, Stephen W 1971 "Gravitationally collapsed objects of very low mass" Monthly Notices of the Royal Astronomical Society 152: 75 Bibcode:1971MNRAS15275H doi:101093/mnras/152175 Cite error: Invalid <ref> tag; name "hawking" defined multiple times with different content see the help page
 ^ a b c Giddings, S B; Thomas, S D 2002 "Highenergy colliders as black hole factories: The End of short distance physics" Physical Review D 65 5: 056010 arXiv:hepph/0106219 Bibcode:2002PhRvD65e6010G doi:101103/PhysRevD65056010
 ^ a b c Dimopoulos, S; Landsberg, G L 2001 "Black Holes at the Large Hadron Collider" Physical Review Letters 87 16: 161602 arXiv:hepph/0106295 Bibcode:2001PhRvL87p1602D doi:101103/PhysRevLett87161602 PMID 11690198
 ^ a b Johnson, George September 11, 2001 "Physicists Strive to Build A Black Hole" The New York Times Retrieved 20100512
 ^ a b "The case for mini black holes" CERN Courier November 2004
 ^ Sciama, Dennis W 1964 "The physical structure of general relativity" Reviews of Modern Physics 36: 463–469 Bibcode:1964RvMP36463S doi:101103/revmodphys36463
 ^ Kibble, Tom W B 1961 "Lorentz invariance and the gravitational field" Journal of Mathematical Physics 2: 212–221 Bibcode:1961JMP2212K doi:101063/11703702
 ^ Popławski, Nikodem J 2010 "Nonsingular Dirac particles in spacetime with torsion" Physics Letters B 690: 73–77 arXiv:09101181 Bibcode:2010PhLB69073P doi:101016/jphysletb201004073
 ^ Stephen Hawking, "new doomsday warning"
 ^ Helfer, A D 2003 "Do black holes radiate" Reports on Progress in Physics 66 6: 943–1008 arXiv:grqc/0304042 Bibcode:2003RPPh66943H doi:101088/00344885/66/6/202
 ^ Susskind, L 2008 The Black Hole War: My battle with Stephen Hawking to make the world safe for quantum mechanics New York: Little, Brown ISBN 9780316016407
 ^ MacGibbon, J H 1987 "Can Planckmass relics of evaporating black holes close the Universe" Nature 329: 308–309 Bibcode:1987Natur329308M doi:101038/329308a0
 ^ Barrau, A 2000 "Primordial black holes as a source of extremely high energy cosmic rays" Astroparticle Physics 12 4: 269–275 arXiv:astroph/9907347 Bibcode:2000APh12269B doi:101016/S0927650599001036
 ^ McKee, M 30 May 2006 "Satellite could open door on extra dimension" New Scientist
 ^ "Fermi Gamma Ray Space Telescope: "Mini" black hole detection"
 ^ Khriplovich, I B; Pomeransky, A A; Produit, N; Ruban, G Yu 2008 "Can one detect passage of small black hole through the Earth" Physical Review D 77 6: 064017 arXiv:07103438 Bibcode:2008PhRvD77f4017K doi:101103/PhysRevD77064017
 ^ Khriplovich, I B; Pomeransky, A A; Produit, N; Ruban, G Yu 2008 "Passage of small black hole through the Earth Is it detectable" 0801: 4623 arXiv:08014623 Bibcode:2008arXiv08014623K
 ^ Cain, Fraser 20 June 2007 "Are Microscopic Black Holes Buzzing Inside the Earth" Universe Today
 ^ Schewe, Phillip F; Stein, Ben; Riordon, James September 26, 2001 Bulletin of Physics News American Institute of Physics 558 Missing or empty title= help
 ^ Choptuik, Matthew W; Pretorius, Frans 2010 "Ultrarelativistic Particle Collisions" Phys Rev Lett 104 11: 111101 arXiv:09081780 Bibcode:2010PhRvL104k1101C doi:101103/PhysRevLett104111101 PMID 20366461
 ^ Peng, GX; Wen, XJ; Chen, YD 2006 "New solutions for the colorflavor locked strangelets" Physics Letters B 633 2–3: 314–318 arXiv:hepph/0512112 Bibcode:2006PhLB633314P doi:101016/jphysletb200511081
 ^ Giddings, S B; Mangano, M L 2008 "Astrophysical implications of hypothetical stable TeVscale black holes" Physical Review D 78: 035009 arXiv:08063381 Bibcode:2008PhRvD78c5009G doi:101103/PhysRevD78035009
 ^ Peskin, M E 2008 "The end of the world at the Large Hadron Collider" Physics 1: 14
 ^ Hawking, Stephen 1995 "Virtual Black Holes" Physical Review D 53: 3099–3107 arXiv:hepth/9510029v1 Bibcode:1996PhRvD533099H doi:101103/PhysRevD533099
 ^ Scardigli, Fabio 1999 "Generalized Uncertainty Principle in Quantum Gravity from MicroBlack Hole Gedanken Experiment" Physics Letters B 452: 39–44 arXiv:hepth/9904025 Bibcode:1999PhLB45239S doi:101016/S0370269399001677
 ^ "Quantum Action Principle with GUT November, 2013, Jie Gu suggests Scardigli "
Bibliography
 Page, Don N 15 January 1976 "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole" Physical Review D 13 2: 198–206 Bibcode:1976PhRvD13198P doi:101103/PhysRevD13198: first detailed studies of the evaporation mechanism
 Carr, B J; Hawking, S W 1 August 1974 "Black holes in the early universe" Monthly Notices of the Royal Astronomical Society 168 2: 399–415 arXiv:12092243 Bibcode:1974MNRAS168399C doi:101093/mnras/1682399: links between primordial black holes and the early universe
 A Barrau et al, Astron Astrophys 388 2002 676, Astron Astrophys 398 2003 403, Astrophys J 630 2005 1015 : experimental searches for primordial black holes thanks to the emitted antimatter
 A Barrau & G Boudoul, Review talk given at the International Conference on Theoretical Physics TH2002 : cosmology with primordial black holes
 A Barrau & J Grain, Phys Lett B 584 2004 114 : searches for new physics quantum gravity with primordial black holes
 P Kanti, Int J Mod Phys A19 2004 4899 : evaporating black holes and extra dimensions
 D Ida, Ky Oda & SCPark, : determination of black hole's life and extra dimensions
 Sabine Hossenfelder: What Black Holes Can Teach Us, hepph/0412265
 L Modesto, PhysRevD70124009: Disappearance of Black Hole Singularity in Quantum Gravity
 P Nicolini, A Smailacic, E Spallucci, jphysletb200511004: Noncommutative geometry inspired Schwarzschild black hole
 A Bonanno, M Reuter, PhysRevD73083005: Spacetime Structure of an Evaporating Black Hole in Quantum Gravity
 Fujioka, Shinsuke; et al 18 October 2009 "Xray astronomy in the laboratory with a miniature compact object produced by laserdriven implosion" Nature Physics 5 11: 821–825 arXiv:09090315 Bibcode:2009NatPh5821F doi:101038/nphys1402 : Xray astronomy in the laboratory with a miniature compact object produced by laserdriven implosion
 Harrison, B K; Thorne, K S; Wakano, M; Wheeler, J A Gravitation Theory and Gravitational Collapse, Chicago: University of Chicago Press, 1965 pages 8081
External links
 Astrophysical implications of hypothetical stable TeVscale black holes
 A Barrau & J Grain, The Case for mini black holes: a review of the searches for new physics with micro black holes possibly formed at colliders CERN Courier Nov 12, 2004
 Mini Black Holes Might Reveal 5th Dimension – Ker Than Spacecom June 26, 2006 10:42am ET
 Doomsday Machine Large Hadron Collider – A scientific essay about energies, dimensions, black holes, and the associated public attention to CERN, by Norbert Frischauf also available as Podcast
 

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