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MORRIS-THORNE TRAVERSABLE WORMHOLE WITH A GENERIC COSMOLOGICAL CONSTANT

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 >