X iv : g r - qc / 0 70 10 32 v 2 1 4 M ay 2 00 7 Wormholes with varying equation of state parameter

We propose wormholes solutions by assuming space dependent equation of state parameter. Our models show that the existence of wormholes is supported by phantom energy. Here the phantom energy is characterized by variable equation state parameter. This averaged null energy condition (ANEC) violating phantom energy can be reduced as desired. A Wormhole is a 'tunnel' through curved spacetime, connecting two widely separated regions of our Universe or even of different Universe. In a pioneer work, Morris and Thorne [1] observed, to hold a wormhole open, one has usually used an exotic matter, which violates the well known energy conditions. The exotic matter is a hypothetical form of matter that has either negative energy density or positive energy density which produces negative pressure / tension. In last few years, exotic matter has been becoming an active area of research in wormhole physics [2]. Since all known matters obey the null energy, T µν k µ k ν > 0, where T µν is the energy stress tensor and k µ any null vector, several authors [3] have considered scalar tensor theories to build wormhole like spacetime with the presence of ordinary matter in which scalar field may play the role of exotic matter. In an interesting paper, Vollick has shown how to produce exotic matter using scalar field [4]. Recent astrophysical observations indicated that the Universe at present is accelerating. There are different ways of evading these unexpected behavior. Most of these attempts focus on Alternative gravity theories or the supposition of existence of a hypothetical dark energy with a positive energy density and a negative pressure [5]. The matter with the property, energy density, ρ > 0 but pressure p < −ρ < 0 is known as Phantom Energy. The Phantom Energy violates the null energy condition what is needed to support traversable wormholes. So phantom energy may play a possible role for constructing wormhole like spacetime.