@MISC{Li00twoopen, author = {Li-xin Li}, title = {Two Open Universes Connected by a Wormhole: Exact Solutions}, year = {2000} }

Share

OpenURL

Abstract

In this paper I present a spacetime of two open universes connected by a Lorentzian wormhole. The spacetime has the following features: (1) It can exactly solve the Einstein equations; (2) The weak energy condition is satisfied everywhere; (3) It has a topology of R2 × Tg (g ≥ 2); (4) It has no event horizons. Key words: topology, wormhole, cosmology 1 Wormholes (or quantum foams) could play important roles on both microscopic and macroscopic scales in the realm of classical and quantum gravity [1, 2, 3, 4]. Field lines trapped in wormholes have led to the concepts of “mass without mass ” and “charge without charge ” [1, 2]. In the context of Euclidean quantum gravity, Euclidean wormholes arise from topology change on the Planckian scales, which have been proposed to cause the loss of quantum coherence or to fix coupling constants [3, 4]. (However, see the recent discussions of Hawking [5].) More interestingly, Morris, Thorne, and Yurtsever [6] (see also Novikov [7]) have shown that a Lorentzian wormhole can be transformed into a time machine (i.e., a spacetime with closed timelike curves). Morris and Thorne [8] have also considered the possibility of using Lorentzian wormholes as tools for interstellar travel. Applications of wormholes in cosmology have also been investigated [9, 10]. In this paper I focus on Lorentzian wormholes, which are essentially the time-development of three-dimensional wormholes [11, 12]. Such kind of spacetimes exhibit wormhole structures on their spacelike foliations, the wormholes either connect one universe to another universe or connect one region to another distant region in the same universe. As far as I am aware, almost all of the Lorentzian wormhole solutions discovered in literatures have two-dimensional spacelike cross-sections with a topology of S2. With very generic arguments, Morris and Thorne [8] have shown that for static, spherically symmetric, and traversable (i.e., having no event horizons) wormholes the weak energy condition must be violated near the wormhole