Self sustained phantom wormholes in semi-classical gravity

TL;DR

This paper explores the theoretical possibility of self-sustained phantom wormholes in semi-classical gravity, analyzing models with a radial-dependent equation of state and quantum fluctuation effects to understand their structure and stability.

Contribution

It introduces models of phantom wormholes with a radial-dependent equation of state and investigates their self-sustainability via quantum fluctuations, extending previous static constant EoS approaches.

Findings

Phantom energy can support traversable wormholes near the throat.

Radial dependence of the EoS parameter is necessary for self-consistent solutions.

Quantum fluctuations can act as a source for sustaining wormhole geometries.

Abstract

A possible candidate for the late time accelerated expanding Universe is phantom energy, which possesses rather bizarre properties, such as the prediction of a Big Rip singularity and the violation of the null energy condition. The latter is a fundamental ingredient of traversable wormholes, and it has been shown that phantom energy may indeed sustain these exotic geometries. Inspired by the evolving dark energy parameter crossing the phantom divide, we consider in this work a varying equation of state parameter dependent on the radial coordinate, i.e., $\omega(r)=p(r)/\rho(r)$. We shall impose that phantom energy is concentrated in the neighborhood of the throat, to ensure the flaring out condition, and several models are analyzed. We shall also consider the possibility that these phantom wormholes be sustained by their own quantum fluctuations. The energy density of the graviton one loop contribution to a classical energy in a phantom wormhole background and the finite one loop energy density are considered as a self-consistent source for these wormhole geometries. The latter semi-classical approach prohibits solutions with a constant equation of state parameter, which further motivates the imposition of a radial dependent parameter, $\omega(r)$, and only permits solutions with a steep positive slope proportional to the radial derivative of the equation of state parameter, evaluated at the throat. The size of the wormhole throat as a function of the relevant parameters is also explored.