New asymptotically flat phantom wormhole solutions

TL;DR

This paper presents new asymptotically flat wormhole solutions supported by phantom energy, demonstrating the possibility of constructing such wormholes with minimal energy condition violation without the need for surgical matching.

Contribution

The authors introduce novel asymptotically flat wormhole solutions supported by phantom energy, extending previous models and allowing for arbitrarily small amounts of exotic matter.

Findings

Existence of asymptotically flat wormholes supported by phantom energy.

Construction of solutions with vanishing energy density and pressures at large distances.

Possibility to minimize the amount of energy condition violating matter.

Abstract

A possible cause of the late-time cosmic acceleration is an exotic fluid with an equation of state lying within the phantom regime, i.e., $w=p/\rho <-1$. The latter violates the null energy condition, which is a fundamental ingredient in wormhole physics. Thus, cosmic phantom energy may, in principle, provide a natural fluid to support wormholes. In this work, we find new asymptotically flat wormhole solutions supported by the phantom energy equation of state, consequently extending previous solutions. Thus, there is no need to surgically paste the interior wormhole geometry to an exterior vacuum spacetime. In the first example, we carefully construct a specific shape function, where the energy density and pressures vanish at large distances as $\sim 1/r^{n}$, with $n>0$. We also consider the "volume integral quantifier", which provides useful information regarding the total amount of energy condition violating matter, and show that, in principle, it is possible to construct asymptotically flat wormhole solutions with an arbitrary small amount of energy condition violating matter. In the second example, we analyse two equations of state, i.e., $p_r=p_r(\rho)$ and $p_t=p_t(\rho)$, where we consider a specific integrability condition in order to obtain exact asymptotically flat wormhole solutions. In the final example, we postulate a smooth energy density profile, possessing a maximum at the throat and vanishing at spatial infinity.