Imaginary wormholes

Using a Friedman-Robinson-Walker minisuperspace model with a minimally coupled homogeneous scalar field we search for, and discover, wormhole-type solutions, which connect two asymptotically flat euclidean spaces, when (a) V = 1 4λε{lunate}⁴, and (b) V = 1 2m²ε{lunate}² + 1 4λε{lunate}⁴. For these potentials, stationary configurations satisfying the boundary conditions of asymptotic flatness necessitate that the scalar field be imaginary. Each solution found can be labeled by an asymptotic constant; however, in distinction from all previously found wormhole solutions, none possess a conserved charge. In the case of potential (a), all solutions found have negative actions, whereas for potential (b), there exist regions of the (m,, λ) parameter space for which the solutions have negative, zero, and positive action. Major ramifications implied by the discovery of these new wormholes solutions are the following: Firstly, the existence of such solutions dispels a longstanding conjecture that euclidean wormholes must possess a conserved charge. Secondly, their existence also dispels a conjecture made by Halliwell and Hartle regarding the behaviour of the real part of the action for wormholes possessing complex geometries. As a result, the criterion proposed by Halliwell and Hartle, for choosing those wormhole saddle-points of the action which should be included into the complex contour of integration, must be augmented to include the effects of complex matter fields. Thirdly, these new wormholes may also seriously undermine current arguments concerning the resolution of the "large-wormhole problem" of Fischler and Susskind in field theories that allow such wormholes to occur.