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This paper discusses traversable wormholes in a dark-energy setting by starting with a model due to Sung-Won Kim. This model, based on the Friedmann–Lemaître–Robertson–Walker model, is combined with a generalized Kaluza–Klein model. It is well known that phantom dark energy can in principle support traversable wormholes due to the violation of the null energy condition (NEC), a necessary condition for holding a wormhole open. Since the phantom divide constitutes a serious barrier, we retain the dark-energy assumption a′′(t)>0but stay below the phantom divide. To show that the violation of the NEC can only come from the fifth dimension requires a careful analysis of the scale factor a(t). While needed in the overall model, certain 1-forms lack this scale factor since the extra dimension, often assumed to be compactified, would not be affected by the cosmological expansion. The result is a viable wormhole model of the Sung-Won-Kim type. Our main conclusion involves Morris–Thorne wormholes: due to the Kaluza–Klein gravity, we obtain a valid wormhole solution without crossing the phantom divide.

In this paper, a Banados-Teitelboim-Zanelli (BTZ) black hole [Phys. Rev. Lett. 69, 1849 (1992)] is constructed from an exact solution of the Einstein field equations in a (2 + 1)--dimensional anti--de Sitter spacetime in the context of noncommutative geometry. The BTZ black hole turns out to have either two horizons, no horizon, or a single horizon corresponding to a minimal mass. Certain thermodynamical properties are investigated, including Hawking temperature, entropy, and heat capacity. Also discussed is the geodesic structure of BTZ black holes for both massless and massive particles. In particular, it is shown that bound orbits for test particles are possible. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain exact solutions of the Einstein field equations describing traversable wormholes supported by phantom energy. Their relationship to exact solutions in the literature is also discussed as well as the conditions required to determine such solutions.

In this note Krasnoselskii's iteration procedure

In the first part of the paper conditions for the existence of ordinary and higher order fixed points of individual and commutative families of nonlinear operators are obtained. The second part deals with the existence of fixed points of an operator $ T:C \to X$ and the weak topology in $ X$ The convergence to fixed points of sequences of successive approximations is considered in both parts.

Noncommutative geometry, an off shoot of string theory, replaces pointlike structures with smeared objects and has recently been extended to higher dimensions. The purpose of this paper is to obtain wormhole solutions with this extended noncommutative geometry as a background. It is found through this investigation that wormhole solutions exist in the usual four, as well as in five dimensions, but they do not exist in higher-dimensional spacetimes. [ABSTRACT FROM AUTHOR]