Traversable wormholes supported by holographic dark energy with a modified equation of state

Abstract

Inspired by holographic dark energy models, we explore various energy density profiles as potential sources for creating traversable wormholes. Because these energy densities are all positive, we introduce an equation of state in the form $p_r\left(r\right)={\omega }_r\left(r\right)\rho \left(r\right)$. We find that achieving Zero Tidal Forces requires ${\omega }_r\left(r\right)$ to become infinite as r approaches infinity. To solve this issue, we introduce appropriate modifications on the function ${\omega }_r\left(r\right)$ in such a way to obtain a finite result everywhere. These modifications do not affect the behavior of the equation of state near the wormhole's throat. Surprisingly, all dark energy profiles end up in the phantom region. Among the profiles we consider, only one does not require changes to ${\omega }_r\left(r\right)$ to achieve Zero Tidal Forces. This profile is also consistent with the presence of a Global Monopole.