New Features of Extended Wormhole Solutions in the Scalar Field Gravity Theories

The present paper reports interesting new features that wormhole solutions in the scalar field gravity theory have. To demonstrate these, we obtain, by using a slightly modified form of the Matos-Nunez algorithm, an extended class of asymptotically flat wormhole solutions belonging to 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 Ellis class III solution, the latter 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 \delta;. 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 analyses reported here have wider applicability in that they can very well be adopted in other theories, including in the string theory.Comment: 19 page

Stable States of Ferroelectric Smectic C* Liquid Crystal Confined between Patterned Surfaces

In this study we consider equilibrium states in a monolayered sample of ferroelectric smectic C∗ confined between two differently patterned substrates with strong anchoring under the applied electric field. By using the continuum theory for a "bookshelf" aligned sample of ferroelectric liquid crystal, we obtain elliptic sine-Gordon equation. It is shown that due to the patterned structure of the substrates, competing boundary conditions in the thin film generate a specific alignment of liquid crystals, which can be controlled by the electric field. This theoretical finding is described as a system with harmonically coupled atoms with an external potential within the framework of the Frenkel-Kontorova model

Frequency voltage controlled light transmittance in ferroelectric liquid crystal cells

Light transmittance of a short-pitch deformed-helix ferroelectric liquid crystal cell was numerically studied when low and high voltage frequencies ($\simeq 1$ kHz and $\simeq 100$ kHz, respectively) are applied to the cell. The reported finding in the decay of light transmittance at increasing frequency is obtained due to reasonable simplifications of the temporal dependence of director's azimuthal angle. By taking experimentally known data, we numerically demonstrate that the increase in temperature of ferroelectric liquid crystals yields an insignificant change of light transmittance within all visible spectra