Quantum Gravity

Anisotropic Structures and Wormholes with Loop Quantum Gravity Holonomy Corrections - DeBenedictis, Andrew Phys.Rev. D84 (2011) 104030 arXiv:1108.0116 [gr-qc]

A possible picture for the space-time foam. Space-time that seems smooth on large scales (left) may actually be endowed with fluctuating topologies (represented by handles on the right) due to quantum gravity effects. One of the simplest models for such a handle is the wormhole.

Schematics of topology changing space-times via wormhole formation. Figure a) represents topology change via the formation of an inter-universe wormhole. Figure b) represents topology change via the formation of an intra-universe wormhole. The points p represent the critical point of the topology change, where quantum gravitation effects are expected to become important. This sort of topology change is thought to be ubiquitous at the Planck scale.

Wormhole profile curve,

Wormhole profile curve, P±(r), in the θ=π/2 submanifold. The wormhole is generated via rotation about the x-axis (inset).

Wormhole profile curve in the θ=π/2 submanifold using the rotated coordinate system. The profile function is given by r=Q(x)=P−1(x) and the radius of the throat is Q0. As before, the wormhole is generated via rotation about the x-axis (inset). Only a single profile function Q(x) is needed now and the densitized triad components are finite at the throat radius.

Symmetric wormhole models with Q(x)=α0cosh(x/x0). The parameters are as follows: Figure a): α0=0.38,x0=0.86, figure b): A close up of the throat region of the previous figure, figure c): α0=0.005,x0=0.06, d): α0=0.3537,x0=0.5. In all cases γ≈0.27 and ℓ\tiny{p} was set to 0.1 to exaggerate the differences to make them easier to see.

Non-symmetric wormhole models with

Q(x)=α0cosh(x/x0)+β0x3. The parameters are as follows: Figure a): α0=0.25,x0=0.5,β0=0.5, figure b): α0=0.305,x0=0.4,β0=−0.95. In both cases γ≈0.27 and ℓ\tiny{p} was set to 0.1 to exaggerate the differences to make them easier to see.