Toy Model of an Inflating Wormhole
There is a possibility that the laws of quantum field theory and general relativity might allow for the existence of wormholes. These can be thought of as "bridges" connecting two otherwise distant regions of space. It is unknown if negative energy in a quantity required to support macroscopic transversable wormholes exists. Spatial hypersurfaces are shown to illustrate the change in size of the wormhole with time through embedding diagrams.
The metric is spherically symmetric, static and transversable in the sense introduced by Morris and Thorne, with an exponential deSitter scale factor multiplying the spatial part
— cosmological constant
— redshift function has no effect
— shape function choice 1
— shape function choice 2
— throat size
— location of the throat
Coordinates with bar correspond to embedding space and "scale" exponentially with time.
— in terms of , embedding function in choice 1
— ensures that this ratio is time-independent in choice 1
— ensures that this ratio is time-independent in choice 2
— the usual "lift" function and embedding function in choice 2
T. Roman, "The Inflation Wormhole: A Mathematica Animation," Computers in Physics, 8(4), 1994 pp. 480.