Traversable Schwarzschild-like wormholes

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 r → ∞ 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 β-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.

Minimally deformed wormholes

“…: V,-vol of linear [33] as well as non-linear electrodynamics [34][35][36]. Moreover, wormhole solutions with other type of symmetries have been investigated in [37][38][39] and also the possibility to obtain a traversable Schwarzschild-like wormhole has been considered [40]. Furthermore, recently [41] was studied and analyzed the behavior of wormhole structures in the realm of dark matter profiles, dark matter Bose-Einstein condensates [42] and non-linear equation of state [43], respectively.…”

On the trajectories of null and timelike geodesics in different wormhole geometries

“…Also, in Ref. [32] Cataldo et al studied a Schwarzschild-like traversable WH which is obtained by putting n = 1 with some slight modification. For geodesics, they showed that a test particle which is radially moving towards the throat always reaches it with zero velocity and at a finite time, while for radially outward geodesics the particle velocity tends to a maximum value, reaching infinity.…”

“…It is interesting to examine whether a timelike or null geodesic can tunnel through the throat in the case Cataldo et al [32] studied, of the motion of test particles in the background of zero tidal force Schwarzschild-like WH spacetime. They showed that particles moving along the radial geodesics reach the throat with zero tidal velocity in finite time, while the particle velocity reaches maximum at infinity if it travels along a radially outward geodesic.…”

Casimir effect in space-times of rotating wormholes

“…Here, the parameter a is for the angular momentum of the wormhole. We also notice that the metric reduces to the one that describes a static Schwarzschild-like wormhole when a = 0 [15]. Thus, if we adopt the transformations indicated just above Eq.…”

“…Despite this, we can get other solutions with specific redshift functions without horizons [13,14]. An interesting generalization in this sense was carried out in [15] by taking a linear shape function, the so-called zero tilde Schwarzschild-like wormhole, which is static and traversable. Another wormhole based on Schwarzschild black hole solution was obtained by Damour and Solodukhin [16], upon modifying the time coefficient of the metric adding to it a very tiny positive constant.…”