Exact Solutions of G-Invariant Chiral Equations

We give a methodology for solving the chiral equations $(\alpha g_{,z} g^{-1})_{,\overline z} + (\alpha g_{,\overline z} g^{-1})_{,z} \ = \ 0$ where $g$ belongs to some Lie group $G$. The solutions are writing in terms of Harmonic maps. The method could be used even for some infinite Lie groups. (Preprint CIEA-gr-94/06)Comment: 8 TeX pages. Seminar presented at the First Mexican-Russian Meeting on Mathematical Physics, Mexico city, 199

Rotating Scalar Field Wormhole

We derive an exact solution to the Einstein's equations with a stress-energy tensor corresponding to an opposite-sign scalar field, and show that such a solution describes the internal region of a rotating wormhole. We also derive an static wormhole asymptotically flat solution and match them on both regions, thus obtaining an analytic solution for the complete space-time. We explore some of the features of these solutions.Comment: Sign of the exponential in equation (10) has been changed. Some typos correcte

Space-Time Curvature Signatures in Bose-Einstein Condensates

We derive a generalized Gross-Pitaevski (GP) equation immersed on a electromagnetic and a weak gravitational field starting from the covariant Complex Klein-Gordon field in a curved space-time. We compare it with the GP equation where the gravitational field is added by hand as an external potential. We show that there is a small difference of order $g z/c^2$ between them that could be measured in the future using Bose-Einstein Condensates (BEC). This represents the next order correction to the Newtonian gravity in a curved space-time.Comment: 4 pages, no figure