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In quantum gravity, a virtual black hole is a hypothetical micro black hole that exists temporarily as a result of a quantum fluctuation of spacetime. 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.
The emergence of virtual black holes at the Planck scale is a consequence of the uncertainty relation
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 Newton's gravitational constant, and c {\displaystyle c} is the speed of light. These uncertainty relations are another form of Heisenberg's uncertainty principle at the Planck scale.
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 }}