Traversable Schwarzschild-like wormholes

Mauricio Cataldo,Luis Liempi,Pablo Rodríguez

doi:10.1140/epjc/s10052-017-5332-5

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 rightarrow infty 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 beta -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.

Highlights

The concept of a bridge connecting two spacetimes may be traced back to a work of Einstein and Rosen [6], who constructed an exact solution of the field equations corresponding to a spacetime of two identical sheets joined by a bridge
We study static traversable wormholes with a linear shape function, which we call Schwarzschild-like wormholes
We have presented new static traversable wormholes, dubbed Schwarzschild-like wormholes, by considering a specific shape function with a linear dependence on the radial coordinate

Summary

Introduction

The concept of a bridge connecting two spacetimes may be traced back to a work of Einstein and Rosen [6], who constructed an exact solution of the field equations corresponding to a spacetime of two identical sheets joined by a bridge. In this paper we consider a slight generalization of Schwarzschild traversable wormholes by considering the radial metric component given by −gr−r1 = Const − r0/r , which implies that the shape function has the linear form b(r ) = a1r + r0, where a1 is a constant parameter. In such a way, we study static traversable wormholes with a linear shape function, which we call Schwarzschild-like wormholes.

The Morris–Thorne wormhole formulation and field equations

Wormholes with linear shape functions

Zero-tidal-force Schwarzschild-like wormholes

Geodesics

Conclusions