Traversability of Schwarzschild-Anti-de Sitter Wormhole in f(T) gravity

TL;DR

This paper investigates the conditions under which Schwarzschild-Anti-de Sitter wormholes in f(T) gravity are traversable, considering energy conditions, tidal forces, and travel times for static and evolving cases.

Contribution

It provides a detailed analysis of traversability criteria for non-asymptotically flat wormholes in f(T) gravity, including energy conditions and travel constraints.

Findings

Nontrivial f(T) form is necessary for wormhole support.

Upper velocity bound derived from tidal force considerations.

Estimated travel times depend on wormhole evolution and size.

Abstract

In this paper we analyze the traversability of static and evolving Schwarzschild-Anti-de Sitter wormholes. The wormhole metric under consideration is not asymptotically flat. Hence one can only embed this metric into the Euclidean space for a limited radius $r_{max}$. For $r>r_{max}$, an exterior vacuum spacetime should be matched to the wormhole spacetime. In the framework of $f(T)$ gravities, we discuss the null energy condition that the matter supporting the wormhole should satisfy and find that the nontrivial form of $f(T)$ is necessary. For the wormholes to be suitable for human to traverse, we consider the tidal force that a traveler would have felt during his trip. This leads to an upper bound of the traveler's velocity. Utilizing the velocity allowed, we will estimate the travel time through the wormhole. In the evolving cases, the wormhole should not be expanding too fast, otherwise the traveler may not be able to arrive at the other side of the wormhole. Besides this, for static wormholes, we briefly discuss the geodesics in the plane $\theta=\pi/2$.