New features of extended wormhole solutions in the scalar field gravity theories

This paper reports new interesting features characteristic of wormhole solutions in the scalar field gravity theories. To demonstrate these, using a slightly modified form of the Matos-Nunez algorithm, we obtain an extended class of asymptotically flat wormhole solutions belonging to the Einstein minimally coupled scalar field theory. Generally, solutions in these theories do not represent traversable wormholes due to the occurrence of curvature singularities. However, the Ellis I solution of the Einstein minimally coupled theory, when Wick rotated, yields an Ellis class III solution representing a singularity-free traversable wormhole. We see that Ellis I and III are not essentially independent solutions. The Wick-rotated seed solutions, extended by the algorithm, contain two new parameters a and δ. The effect of the parameter a on the geodesic motion of test particles reveals some remarkable features. By arguing for Sagnac effect in the extended Wick-rotated solution, we find that the parameter a can indeed be interpreted as a rotation parameter of the wormhole. The analysis reported here has wide applicability, for it can be adopted in other scalar field theories, including string theory