Equatorial cross section of the Ellis wormhole, a catenoid
The Ellis wormhole is the special case of the Ellis drainhole in which the 'ether' is not flowing and there is no gravity. What remains is a pure traversable wormhole comprising a pair of identical twin, nonflat, three-dimensional regions joined at a two-sphere, the 'throat' of the wormhole. As seen in the image shown, two-dimensional equatorial cross sections of the wormhole are catenoidal 'collars' that are asymptotically flat far from the throat. There being no gravity in force, an inertial observer (test particle) can sit forever at rest at any point in space, but if set in motion by some disturbance will follow a geodesic of an equatorial cross section at constant speed, as would also a photon. This phenomenon shows that in space-time the curvature of space has nothing to do with gravity (the 'curvature of time’, one could say).
As a special case of the Ellis drainhole, itself a 'traversable wormhole', the Ellis wormhole dates back to the drainhole's discovery in 1969 (date of first submission) by H. G. Ellis,[1]
and independently at about the same time by K. A. Bronnikov.[2]
Ellis and Bronnikov derived the original traversable wormhole as a solution of the Einstein vacuum field equations augmented by inclusion of a scalar field minimally coupled to the geometry of space-time with coupling polarity opposite to the orthodox polarity (negative instead of positive). Some years later M. S. Morris and K. S. Thorne manufactured a duplicate of the Ellis wormhole to use as a tool for teaching general relativity,[3]
asserting that existence of such a wormhole required the presence of 'negative energy', a viewpoint Ellis had considered and explicitly refused to accept, on the grounds that arguments for it were unpersuasive.[1]
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H. G. Ellis (1973). "Ether flow through a drainhole: A particle model in general relativity". Journal of Mathematical Physics. 14 (1): 104–118. Bibcode:1973JMP....14..104E. doi:10.1063/1.1666161.
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K. A. Bronnikov (1973). "Scalar-tensor theory and scalar charge". Acta Physica Polonica. B4: 251–266.
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M. S. Morris; K. S. Thorne (1988). "Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity". American Journal of Physics. 56 (5): 395–412. Bibcode:1988AmJPh..56..395M. doi:10.1119/1.15620.
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