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virtual black hole wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 see also 2 references 3 further reading toggle the table of contents virtual black hole 10 languages العربية беларуская español فارسی français 한국어 português русский tiếng việt 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia black holes appearing from quantum spacetime fluctuations this article may be too technical for most readers to understand please help improve it to make it understandable to non experts without removing the technical details december 2020 learn how and when to remove this message in quantum gravity a virtual black hole 1 is a hypothetical micro black hole that exists temporarily as a result of a quantum fluctuation of spacetime 2 it is an example of quantum foam and is the gravitational analog of the virtual electron positron pairs found in quantum electrodynamics theoretical arguments suggest that virtual black holes should have mass on the order of the planck mass lifetime around the planck time and occur with a number density of approximately one per planck volume 3 the emergence of virtual black holes at the planck scale is a consequence of the uncertainty relation 4 δ r μ δ x μ ℓ p 2 ℏ g c 3 displaystyle delta r_ mu delta x_ mu geq ell _ p 2 frac hbar g c 3 where r μ displaystyle r_ mu is the radius of curvature of spacetime small domain x μ displaystyle x_ mu is the coordinate of the small domain ℓ p displaystyle ell _ p is the planck length ℏ displaystyle hbar is the reduced planck constant g displaystyle g is the newtonian constant of gravitation and c displaystyle c is the speed of light these uncertainty relations are another form of heisenberg s uncertainty principle at the planck scale proof indeed these uncertainty relations can be obtained on the basis of einstein s equations g μ ν λ g μ ν 8 π g c 4 t μ ν displaystyle g_ mu nu lambda g_ mu nu 8 pi g over c 4 t_ mu nu where g μ ν r μ ν r 2 g μ ν displaystyle g_ mu nu r_ mu nu r over 2 g_ mu nu is the einstein tensor which combines the ricci tensor the scalar curvature and the metric tensor λ displaystyle lambda is the cosmological constant а t μ ν displaystyle t_ mu nu is the energy momentum tensor of matter π displaystyle pi is the mathematical constant pi c displaystyle c is the speed of light and g displaystyle g is the newtonian constant of gravitation einstein suggested that physical space is riemannian i e curved and therefore put riemannian geometry at the basis of the theory of gravity a small region of riemannian space is close to flat space 5 for any tensor field n μ ν displaystyle n_ mu nu we may call n μ ν g displaystyle n_ mu nu sqrt g a tensor density where g displaystyle g is the determinant of the metric tensor g μ ν displaystyle g_ mu nu the integral n μ ν g d 4 x displaystyle int n_ mu nu sqrt g d 4 x is a tensor if the domain of integration is small it is not a tensor if the domain of integration is not small because it then consists of a sum of tensors located at different points and it does not transform in any simple way under a transformation of coordinates 6 here we consider only small domains this is also true for the integration over the three dimensional hypersurface s ν displaystyle s nu thus the einstein field equations for a small spacetime domain can be integrated by the three dimensional hypersurface s ν displaystyle s nu have 4 7 1 4 π g μ ν λ g μ ν g d s ν 2 g c 4 t μ ν g d s ν displaystyle frac 1 4 pi int left g_ mu nu lambda g_ mu nu right sqrt g ds nu 2g over c 4 int t_ mu nu sqrt g ds nu since integrable space time domain is small we obtain the tensor equation r μ 2 g c 3 p μ displaystyle r_ mu frac 2g c 3 p_ mu where p μ 1 c t μ ν g d s ν displaystyle p_ mu frac 1 c int t_ mu nu sqrt g ds nu is the component of the 4 momentum of matter r μ 1 4 π g μ ν λ g μ ν g d s ν displaystyle r_ mu frac 1 4 pi int left g_ mu nu lambda g_ mu nu right sqrt g ds nu is the component of the radius of curvature small domain the resulting tensor equation can be rewritten in another form since p μ m c u μ displaystyle p_ mu mc u_ mu then r μ 2 g c 3 m c u μ r s u μ displaystyle r_ mu frac 2g c 3 mc u_ mu r_ s u_ mu where r s displaystyle r_ s is the schwarzschild radius u μ displaystyle u_ mu is the 4 speed m displaystyle m is the gravitational mass this record reveals the physical meaning of the r μ displaystyle r_ mu values as components of the gravitational radius r s displaystyle r_ text s in a small area of space time is almost flat and this equation can be written in the operator form r μ 2 g c 3 p μ 2 g c 3 i ℏ x μ 2 i ℓ p 2 x μ displaystyle hat r _ mu frac 2g c 3 hat p _ mu frac 2g c 3 i hbar frac partial partial x mu 2i ell _ p 2 frac partial partial x mu or the basic equation of quantum gravity 4 7 2 i ℓ p 2 x μ ψ x μ r μ ψ x μ displaystyle 2i ell _ p 2 frac partial partial x mu psi x_ mu rangle hat r _ mu psi x_ mu rangle then the commutator of operators r μ displaystyle hat r _ mu and x μ displaystyle hat x _ mu is r μ x μ 2 i ℓ p 2 displaystyle hat r _ mu hat x _ mu 2i ell _ p 2 from here follow the specified uncertainty relations δ r μ δ x μ ℓ p 2 displaystyle delta r_ mu delta x_ mu geq ell _ p 2 substituting the values of r μ 2 g c 3 m c u μ displaystyle r_ mu frac 2g c 3 m c u_ mu and ℓ p 2 ℏ g c 3 displaystyle ell _ p 2 frac hbar g c 3 and reducing identical constants from two sides we get heisenberg s uncertainty principle δ p μ δ x μ δ m c u μ δ x μ ℏ 2 displaystyle delta p_ mu delta x_ mu delta mc u_ mu delta x_ mu geq frac hbar 2 in the particular case of a static spherically symmetric field and static distribution of matter u 0 1 u i 0 i 1 2 3 displaystyle u_ 0 1 u_ i 0 i 1 2 3 and have remained δ r 0 δ x 0 δ r s δ r ℓ p 2 displaystyle delta r_ 0 delta x_ 0 delta r_ text s delta r geq ell _ p 2 where r s displaystyle r_ text s is the schwarzschild radius r displaystyle r is the radial coordinate here r 0 r s displaystyle r_ 0 r_ text s and x 0 c t r displaystyle x_ 0 c t r since the matter moves with velocity of light in the planck scale last uncertainty relation allows make us some estimates of the equations of general relativity at the planck scale for example the equation for the invariant interval d s displaystyle ds в in the schwarzschild solution has the form d s 2 1 r s r c 2 d t 2 d r 2 1 r s r r 2 d ω 2 sin 2 ω d φ 2 displaystyle ds 2 left 1 frac r_ text s r right c 2 dt 2 frac dr 2 1 r_ text s r r 2 d omega 2 sin 2 omega d varphi 2 substitute according to the uncertainty relations r s ℓ p 2 r displaystyle r_ text s approx ell _ p 2 r we obtain d s 2 1 ℓ p 2 r 2 c 2 d t 2 d r 2 1 ℓ p 2 r 2 r 2 d ω 2 sin 2 ω d φ 2 displaystyle ds 2 approx left 1 frac ell _ p 2 r 2 right c 2 dt 2 frac dr 2 1 ell _ p 2 r 2 r 2 d omega 2 sin 2 omega d varphi 2 it is seen that at the planck scale r ℓ p displaystyle r ell _ p space time metric is bounded below by the planck length division by zero appears and on this scale there are real and virtual planckian black holes similar estimates can be made in other equations of general relativity for example analysis of the hamilton jacobi equation for a centrally symmetric gravitational field in spaces of different dimensions with help of the resulting uncertainty relation indicates a preference energy profitability for three dimensional space for the emergence of virtual black holes quantum foam the basis of the fabric of the universe 4 7 this may have predetermined the three dimensionality of the observed space prescribed above uncertainty relation valid for strong gravitational fields as in any sufficiently small domain of a strong field space time is essentially flat if virtual black holes exist they provide a mechanism for proton decay 8 this is because when a black hole s mass increases via mass falling into the hole and is theorized to decrease when hawking radiation is emitted from the hole the elementary particles emitted are in general not the same as those that fell in therefore if two of a proton s constituent quarks fall into a virtual black hole it is possible for an antiquark and a lepton to emerge thus violating conservation of baryon number 3 9 the existence of virtual black holes aggravates the black hole information loss paradox as any physical process may potentially be disrupted by interaction with a virtual black hole 10 see also edit quantum foam virtual particle quantum tunnelling references edit t hooft gerard october 2018 virtual black holes and space time structure foundations of physics 48 10 1134 1149 bibcode 2018foph 48 1134t doi 10 1007 s10701 017 0133 0 issn 0015 9018 s2cid 189842716 hawking s w march 1996 virtual black holes physical review d 53 6 3099 3107 arxiv hep th 9510029 bibcode 1996phrvd 53 3099h doi 10 1103 physrevd 53 3099 issn 0556 2821 pmid 10020307 1 2 adams fred c kane gordon l mbonye manasse perry malcolm j may 2001 proton decay black holes and large extra dimensions international journal of modern physics a 16 13 2399 2410 arxiv hep ph 0009154 bibcode 2001ijmpa 16 2399a doi 10 1142 s0217751x0100369x issn 0217 751x 1 2 3 4 klimets a p november 2023 quantum gravity pdf current research in statistics mathematics 2 1 141 155 dirac 1975 p 9 dirac 1975 p 37 1 2 3 klimets alexander 2017 on the fundamental role of massless form of matter in physics quantum gravity pdf fizika b 9 23 42 bambi cosimo freese katherine 2008 dangerous implications of a minimum length in quantum gravity classical and quantum gravity 25 19 195013 arxiv 0803 0749 bibcode 2008cqgra 25s5013b doi 10 1088 0264 9381 25 19 195013 hdl 2027 42 64158 issn 0264 9381 s2cid 2040645 al modlej abeer alsaleh salwa alshal hassan ali ahmed farag 2019 proton decay and the quantum structure of space time canadian journal of physics 97 12 1317 1322 arxiv 1903 02940 bibcode 2019cajph 97 1317a doi 10 1139 cjp 2018 0423 hdl 1807 96892 issn 0008 4204 s2cid 119507878 giddings steven b 1995 the black hole information paradox arxiv hep th 9508151 further reading edit dirac p a m 1975 general theory of relativity new york wiley isbn 978 0 471 21575 2 cite book cs1 maint publisher location link v t e black holes outline types btz black hole schwarzschild rotating charged virtual kugelblitz supermassive primordial direct collapse rogue malament hogarth spacetime size micro extremal electron stellar microquasar intermediate mass supermassive active galactic nucleus quasar lqg blazar bl lac fsrq formation stellar evolution gravitational collapse neutron star related links tolman oppenheimer volkoff limit oppenheimer snyder model white dwarf related links supernova micronova hypernova related links gamma ray burst binary black hole quark star supermassive star quasi star supermassive dark star x ray binary low mass properties astrophysical jet gravitational singularity ring singularity bkl singularity shock singularity theorems event horizon photon sphere innermost stable circular orbit ergosphere penrose process blandford znajek process accretion disk hawking radiation gravitational lens microlens cauchy horizon mass inflation bondi accretion m sigma relation quasi periodic oscillation thermodynamics bekenstein bound bousso s holographic bound immirzi parameter schwarzschild radius spaghettification issues information paradox complementarity soft hair cosmic censorship er epr final parsec problem firewall physics holographic principle no hair theorem metrics schwarzschild derivation kerr reissner nordström kerr newman hayward alternatives nonsingular black hole models black star dark star dark energy star gravastar magnetospheric eternally collapsing object planck star q star fuzzball geon analogs optical black hole sonic black hole lists black holes most massive nearest quasars microquasars related outline of black holes black hole initiative black hole starship black holes in fiction big bang big bounce compact star exotic star quark star preon star gravitational waves gamma ray burst progenitors gravity well hypercompact stellar system membrane paradigm naked singularity population iii star supermassive star quasi star supermassive dark star rossi x ray timing explorer superluminal motion timeline of black hole physics white hole wormhole tidal disruption event notable 1es 1927 654 3c 273 a0620 00 at2018hyz centaurus a cygnus x 1 gaia bh1 hercules a markarian 501 ms 0735 6 7421 neve 1 oj 287 phoenix cluster pks 1302 102 pso j030947 49 271757 31 q0906 6930 sagittarius a sdss j0849 1114 swift j1644 57 ton 618 ulas j1342 0928 xte j1118 480 xte j1650 500 category commons this article about theoretical physics is a stub you can help wikipedia by adding missing information v t e retrieved from https en wikipedia org w index php title virtual_black_hole oldid 1368077363 categories quantum gravity black holes theoretical physics stubs hidden categories articles with short description short description matches wikidata wikipedia articles that are too technical from december 2020 all articles that are too technical cs1 maint publisher location all stub articles this page was last edited on 6 august 2026 at 22 10 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy 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