Author : N M Eman, M S Alam, S M Khurshed Alam, Q M R Nizam

International Journal of Scientific & Engineering Research Volume 4, Issue 10, October-2013

ISSN 2229-5518

Download Full Paper : PDF**Abstruct**The static and spherically symmetric Morris-Thorne traversable wormhole solutions in the presence of cosmological constant are analyzed. We matched an interior solution of a spherically symmetric traversable wormhole to a unique exterior vacuum solution at a junction surface. The surface tangential pressure on the thin layer of shell is deduced. The specific wormhole solutions are constructed with generic cosmological constant.

**I INTRODUCTION**Wormholes are handles or tunnels in the spacetime topology connecting two separate and distinct regions of spacetime. These regions may be part of our Universe or of different Universes. The static and spherically symmetric traversable wormhole was first introduced by Morris and Thorne in their classic paper [1]. From the stand point of cosmology,the cosmological constant Λ, served to create a kind of repulsive pressure to yield a stationary Universe. Zel’dovich [2] identified Λ with the vacuum energy density due to quantum fluctuations. Morris-Thorne wormholes with a cosmological constant Λ have been studied extensively, even allowing Λ to be replaced by a space variable scalar field. These wormholes cannot exist, however, if Λ are both space and time dependent. Such a Λ will therefore act as a topological censor.

In this article, we introduce an exact black hole solution of the Einstein field equations in four dimensions with a positive cosmological constant to electromagnetic and conformally coupled scalar fields. This solution is often called a Martinez-Troncoso-Zanelli (MTZ) black hole solution. In agreement with recent observations [3], this black hole only exists for a positive cosmological constant Λ, and if a quartic self-interaction coupling is considered. Static scalar field configurations such as those presented here, which are regular both at the horizon as well as outside, are unexpected in view of the no-hair conjecture [4]. The conformal coupling for the scalar field is the unique prescription that guarantees the validity of the equivalence principle in curved spacetime [5]. In the literature, a number of traversable wormhole solutions with cosmological constant are available [6-21]. A general class of wormhole geometries with a cosmological constant and junction conditions was analyzed by De Benedictis and Das [9], and further explored in higher dimensions [10]. It is of interest to study a positive cosmological constant, as the inflationary phase of the ultra-early universe demands it, and in addition, recent astronomical observations point to 0>Λ. Lobo [12], with the intension of minimizing the exotic matter used, matched a static and spherically symmetric wormhole solution to an exterior vacuum solution with a cosmological constant, and he calculate the surface stresses of the resulting shell and the total amount of exotic matter using a volume integral quantifier [13]. The construction of traversable wormhole solutions by matching an interior wormhole spacetime to an exterior solution, at a junction surface, was analyzed in [13-15]. A thin-shell traversable wormhole, with a zero surface energy density was analyzed in [15], and with generic surface stresses in [14]. A general class of wormhole geometries with a cosmological constant and junction conditions was explored in [9], and a linearized stability analysis for the plane symmetric case with a negative cosmological constant is done in [17].

Morris-Thorne wormholes, with Λ = 0, have two asymptotically flat regions spacetime. By adding a positive cosmological constant0>Λ, the wormholes have two asymptotically de-Sitter regions, and by adding a negative cosmological constant, 0<Λ, the wormholes have two asymptotically anti-de Sitter regions. We analyze asymptotically flat and static traversable Morris-Thorne wormholes in the presence of a cosmological construct. An equation connecting the radial tension at the mouth with the tangential surface pressure of the thin-shell is derived. The structure as well as several physical properties and characteristics of traversable wormholes due to the effects of the cosmological term are studied.

This article is organized as follows: In Sec. II we studied Einstein’s field equations and total stress-energy with a cosmological constant Λ. In Sec. III, we introduce an exact black hole solution with electromagnetic and conformally coupled scalar fields. The junction conditions and the surface tangential pressure are discussed in Sec.

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