Analytical solution of traversable wormholes in the presence of positive cosmological constant

TL;DR

This paper derives an analytical solution for traversable wormholes with a positive cosmological constant using the gravitational decoupling method, revealing modified geometries and energy condition violations.

Contribution

It introduces a new analytical model of traversable wormholes incorporating a positive cosmological constant via the gravitational decoupling approach.

Findings

The solution features a cosmological throat alongside the standard wormhole throat.

The flare-out condition is satisfied at both throats.

Null energy condition violations occur near the throats, enabling traversability.

Abstract

The construction of traversable wormholes (WHs) with a cosmological constant, $\Lambda$, introduces significant challenges and leads to non-trivial modifications of the spacetime geometry. In this work, we obtain an analytical solution describing a traversable WH for $\Lambda>0$ by utilizing the gravitational decoupling (GD) method. In this framework, we consider the Ellis-Bronnikov WH geometry and derive the corresponding deformation induced by the cosmological constant term. In addition to modifying the standard WH throat, this contribution leads to a cosmological throat. The resulting configuration, however, is not asymptotically de Sitter, instead, it exhibits modified asymptotic behaviour. Nevertheless, we verify that the flare-out condition holds at both throats and find violation of the null energy condition in their vicinity, as required for traversable WHs. Traversability is further analyzed by evaluating tidal forces and deriving constraints on the velocity required for safe human passage.