This article may be too technical for most readers to understand. Please help improve ittomake it understandable to non-experts, without removing the technical details. (December 2020) (Learn how and when to remove this message)
|
Inquantum gravity, a virtual black hole[1] is a hypothetical micro black hole that exists temporarily as a result of a quantum fluctuationofspacetime.[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]
where is the radius of curvature of spacetime small domain,
is the coordinate of the small domain,
is the Planck length,
is the reduced Planck constant,
is the Newtonian constant of gravitation, and
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
where 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
Thus, the Einstein field equations for a small spacetime domain can be integrated by the three-dimensional hypersurface Since integrable space-time domain is small, we obtain the tensor equation
where
The resulting tensor equation can be rewritten in another form. Since
where In a small area of space-time is almost flat and this equation can be written in the operator form or
Then the commutator of operators From here follow the specified uncertainty relations
Substituting the values of
In the particular case of a static spherically symmetric field and static distribution of matter
where
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
Substitute according to the uncertainty relations
It is seen that at the Planck scale 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]
This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it. |