00 5 A theoretical construction of wormhole supported by Phantom Energy

A new solution has been presented for the spherically symmetric space time describing wormholes with Phantom Energy. The model suggests that the existence of wormhole is supported by arbitrarily small quantity of Phantom Energy. Wormholes are geometrical structures connecting two distinct space times. It is very interesting object in Modern science as because if traversable wormhole exists , the time machine can be constructed [1]. Wormhole is the solution of Einstein equation and shared by the violation of null energy condition. The matter that characterized the above stress energy tensor is known as exotic matter. There has been a fairly large amount of discussions [2]on wormholes beginning with the work of Morris and Throne[3]. Several authors have discussed wormholes in scalar tensor theory of gravity in which scalar field may play the role of exotic matter [4]. Recently, Researcher are interested to know how much exotic matter is needed to get a traversable wormhole [5-8]. Recent Astrophysical observations indicate 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 [9]. 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 wormhole. Several authors have recently discussed the physical properties and characteristics of traversable worm-holes by taking Phantom Energy as source [10-12]. Recently, Zaslavskii [13] have found a particular exact solution describing wormhole with a linear equation of state , p r < −ρ < 0, p tr > 0 (p r and p tr are radial and transverse