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ill expire on 04 29 8 january 2027 your current ip address is 5 135 42 194 even while globally blocked you will usually still be able to edit pages on meta wiki if you believe you were blocked by mistake you can find additional information and instructions in the stewards block wizard other useful links global blocks help i have been blocked you can view and copy the source of this page short description black holes appearing from quantum spacetime fluctuations technical date december 2020 in quantum gravity a virtual black hole ref name urlvirtual black holes and space time structure springerlink cite journal last t hooft first gerard date october 2018 title virtual black holes and space time structure journal foundations of physics language en volume 48 issue 10 pages 1134 1149 doi 10 1007 s10701 017 0133 0 issn 0015 9018 s2cid 189842716 doi access free bibcode 2018foph 48 1134t ref is a hypothetical micro black hole that exists temporarily as a result of a quantum fluctuation of spacetime ref cite journal last hawking first s w date march 1996 title virtual black holes journal physical review d language en volume 53 issue 6 pages 3099 3107 arxiv hep th 9510029 bibcode 1996phrvd 53 3099h doi 10 1103 physrevd 53 3099 issn 0556 2821 pmid 10020307 ref it is an example of quantum foam and is the gravitation al 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 ref name 2001ijmpa 16 2399a cite journal last1 adams first1 fred c last2 kane first2 gordon l last3 mbonye first3 manasse last4 perry first4 malcolm j date may 2001 title proton decay black holes and large extra dimensions journal international journal of modern physics a language en volume 16 issue 13 pages 2399 2410 arxiv hep ph 0009154 bibcode 2001ijmpa 16 2399a doi 10 1142 s0217751x0100369x issn 0217 751x ref the emergence of virtual black holes at the planck scale is a consequence of the uncertainty relation ref name klimets1 cite journal last klimets first a p date november 2023 title quantum gravity url https www opastpublishers com open access articles quantum gravity pdf journal current research in statistics mathematics volume 2 issue 1 pages 141 155 ref math delta r_ mu delta x_ mu ge ell 2_ p frac hbar g c 3 math where math r_ mu math is the radius of curvature of spacetime small domain math x_ mu math is the coordinate of the small domain math ell_ p math is the planck length math hbar math is the reduced planck constant math g math is the newtonian constant of gravitation and math c math is the speed of light these uncertainty relations are another form of heisenberg s uncertainty principle at the planck scale class toccolours collapsible collapsed width 60 style text align left proof indeed these uncertainty relations can be obtained on the basis of einstein s equations equation box 1 indent equation math g_ mu nu lambda g_ mu nu 8 pi g over c 4 t_ mu nu math cellpadding border border colour 0073cf background colour f5fffa where math g_ mu nu r_ mu nu r over 2 g_ mu nu math is the einstein tensor which combines the ricci tensor the scalar curvature and the metric tensor math lambda math is the cosmological constant а math t_ mu nu math is the energy momentum tensor of matter math pi math is the mathematical constant pi math c math is the speed of light and math g math 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 ref harvnb dirac 1975 p 9 ref for any tensor field math n_ mu nu math we may call math n_ mu nu sqrt g math a tensor density where math g math is the determinant of the metric tensor math g_ mu nu math the integral math int n_ mu nu sqrt g d 4x math 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 ref harvnb dirac 1975 p 37 ref here we consider only small domains this is also true for the integration over the three dimensional hypersurface math s nu math thus the einstein field equations for a small spacetime domain can be integrated by the three dimensional hypersurface math s nu math have ref name klimets1 ref name klimets cite journal last klimets first alexander date 2017 title on the fundamental role of massless form of matter in physics quantum gravity url https philpapers org archive alxotf pdf journal fizika b issue 9 pages 23 42 ref math 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 math since integrable space time domain is small we obtain the tensor equation equation box 1 indent equation math r_ mu frac 2g c 3 p_ mu math cellpadding border border colour 0073cf background colour f5fffa where math p_ mu frac 1 c int t_ mu nu sqrt g ds nu math is the component of the 4 momentum of matter math r_ mu frac 1 4 pi int left g_ mu nu lambda g_ mu nu right sqrt g ds nu math is the component of the radius of curvature small domain the resulting tensor equation can be rewritten in another form since math p_ mu mc u_ mu math then math r_ mu frac 2g c 3 mc u_ mu r_s u_ mu math where math r_s math is the schwarzschild radius math u_ mu math is the 4 speed math m math is the gravitational mass this record reveals the physical meaning of the math r_ mu math values as components of the gravitational radius math r_ text s math in a small area of space time is almost flat and this equation can be written in the operator physics operator form math hat r_ mu frac 2g c 3 hat p_ mu frac 2g c 3 i hbar frac partial partial x mu 2i ell 2_ p frac partial partial x mu math or equation box 1 indent title the basic equation of quantum gravity ref name klimets1 ref name klimets equation math 2i ell 2_ p frac partial partial x mu psi x_ mu rangle hat r_ mu psi x_ mu rangle math cellpadding border border colour 0073cf background colour f5fffa then the commutator of operators math hat r_ mu math and math hat x_ mu math is math hat r_ mu hat x_ mu 2i ell 2_ p math from here follow the specified uncertainty relations equation box 1 indent equation math delta r_ mu delta x_ mu ge ell 2_ p math cellpadding border border colour 0073cf background colour f5fffa substituting the values of math r_ mu frac 2g c 3 m c u_ mu math and math ell 2_ p frac hbar g c 3 math and reducing identical constants from two sides we get heisenberg s uncertainty principle math delta p_ mu delta x_ mu delta mc u_ mu delta x_ mu ge frac hbar 2 math in the particular case of a static spherically symmetric field and static distribution of matter math u_ 0 1 u_i 0 i 1 2 3 math and have remained math delta r_ 0 delta x_ 0 delta r_ text s delta r ge ell 2_ p math where math r_ text s math is the schwarzschild radius math r math is the radial coordinate here math r_0 r_ text s math and math x_0 c t r math 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 math ds math в in the schwarzschild solution has the form math ds 2 left 1 frac r_ text s r right c 2dt 2 frac dr 2 1 r_ text s r r 2 d omega 2 sin 2 omega d varphi 2 math substitute according to the uncertainty relations math r_ text s approx ell 2_p r math we obtain math ds 2 approx left 1 frac ell 2_ p r 2 right c 2dt 2 frac dr 2 1 ell 2_ p r 2 r 2 d omega 2 sin 2 omega d varphi 2 math it is seen that at the planck scale math r ell_p math 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 ref name klimets1 ref name klimets 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 ref name 0803 0749 cite journal last1 bambi first1 cosimo last2 freese first2 katherine year 2008 title dangerous implications of a minimum length in quantum gravity journal classical and quantum gravity volume 25 issue 19 article number 195013 arxiv 0803 0749 bibcode 2008cqgra 25s5013b doi 10 1088 0264 9381 25 19 195013 issn 0264 9381 s2cid 2040645 hdl 2027 42 64158 ref 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 ref name 2001ijmpa 16 2399a ref name 1903 02940 cite journal last1 al modlej first1 abeer last2 alsaleh first2 salwa last3 alshal first3 hassan last4 ali first4 ahmed farag year 2019 title proton decay and the quantum structure of space time journal canadian journal of physics language en volume 97 issue 12 pages 1317 1322 arxiv 1903 02940 bibcode 2019cajph 97 1317a doi 10 1139 cjp 2018 0423 issn 0008 4204 s2cid 119507878 hdl 1807 96892 ref 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 ref cite arxiv eprint hep th 9508151 last1 giddings first1 steven b title the black hole information paradox date 1995 ref see also quantum foam virtual particle quantum tunnelling references reflist further reading cite book last dirac first p a m url https archive org details generaltheoryofr0000dira title general theory of relativity date 1975 publisher new york wiley isbn 978 0 471 21575 2 black holes category quantum gravity category black holes theoretical physics stub pages transcluded onto the current version of this page help template ambox view source template editor protected template article stub box view source template editor protected template asbox view source template editor protected template black holes edit template cite arxiv view source template editor protected template cite book view source fully protected template cite journal view source fully protected template equation box view source semi protected template equation box 1 view source semi protected template harvard citation no brackets view source template editor protected template harvnb view source template editor protected template hlist styles css view source fully protected template icon view source template editor protected template main other view source fully protected template navbox view source template editor protected template pagetype view source fully protected template reflist view source fully protected template reflist styles css view source fully protected template sdcat view source fully protected template short description view source fully protected template short description lowercasecheck view source fully protected template technical view source template editor protected template 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