Elliptic and circular wormholes

Abstract

Two new exact analytical solutions of the euclidean Einstein equations for a minimal massless scalar field and negative cosmological constant have been obtained. These solutions are given in terms of Jacobian elliptic or circular functions, rather than hyperbolic functions, connect large asymptotic regions of maximally-symmetric anti-DeSitter metrics through a microscopic throat, and correspond to negative definite components of the Ricci tensor. Therefore, they describe wormhole-like changes of topology driven by nucleation of baby universes. The quantum state of such elliptic and circular wormholes or handles is discussed in the most interesting inner and asymptotic regions.