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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 electronpositron 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

${\displaystyle \Delta R_{\mu }\Delta x_{\mu }\geq \ell _{P}^{2}={\frac {\hbar G}{c^{3))))$

where ${\displaystyle R_{\mu ))$ is the radius of curvature of spacetime small domain, ${\displaystyle x_{\mu ))$ is the coordinate of the small domain, ${\displaystyle \ell _{P))$ is the Planck length, ${\displaystyle \hbar }$ is the reduced Planck constant, ${\displaystyle G}$ is the Newtonian constant of gravitation, and ${\displaystyle c}$ is the speed of light. These uncertainty relations are another form of Heisenberg's uncertainty principle at the Planck scale.

If virtual black holes exist, they provide a mechanism for proton decay.[7] 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][8]

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.[9]

## References

1. ^ S. W. Hawking (1995) "Virtual Black Holes"
2. ^ a b Fred C. Adams, Gordon L. Kane, Manasse Mbonye, and Malcolm J. Perry (2001), "Proton Decay, Black Holes, and Large Extra Dimensions", Intern. J. Mod. Phys. A, 16, 2399.
3. ^
4. ^
5. ^ a b c Klimets A.P., Philosophy Documentation Center, Western University-Canada, 2017, pp.25–32
6. ^ 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. S2CID 2040645.
7. ^ 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. S2CID 119507878.
8. ^ The black hole information paradox, Steven B. Giddings, arXiv:hep-th/9508151v1.