Eur. Phys. J. C (2017) 77: 748
https://doi.org/10.1140/epjc/s10052-017-5332-5

Regular Article - Theoretical Physics

Traversable Schwarzschild-like wormholes

¹ Departamento de Física, Facultad de Ciencias, Universidad del Bío-Bío, Avenida Collao 1202, Casilla 15-C, Concepción, Chile
² Grupo de Cosmología y Gravitación-UBB, Concepción, Chile
³ Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile
⁴ Facultad de Ingeniería y Tecnología, Universidad San Sebastían, Campus Las Tres Pascualas, Lientur 1457, Concepción, Chile

^* e-mail: mcataldo@ubiobio.cl

Received: 9 April 2017
Accepted: 25 October 2017
Published online: 7 November 2017

Abstract

In this paper we study relativistic static traversable wormhole solutions which are a slight generalization of Schwarzschild wormholes. In order to do this we assume a shape function with a linear dependence on the radial coordinate r. This linear shape function generates wormholes whose asymptotic spacetime is not flat: they are asymptotically locally flat, since in the asymptotic limit spacetimes exhibiting a solid angle deficit (or excess) are obtained. In particular, there exist wormholes which connect two asymptotically non-flat regions with a solid angle deficit. For these wormholes the size of their embeddings in a three-dimensional Euclidean space extends from the throat to infinity. A new phantom zero-tidal-force wormhole exhibiting such asymptotic is obtained. On the other hand, if a solid angle excess is present, the size of the wormhole embeddings depends on the amount of this angle excess, and the energy density is negative everywhere. We discuss the traversability conditions and study the impact of the -parameter on the motion of a traveler when the wormhole throat is crossed. A description of the geodesic behavior for the wormholes obtained is also presented.