Self sustained traversable wormholes and the equation of state

TL;DR

This paper analyzes the quantum corrections to traversable wormholes with a specific equation of state, using variational and zeta function regularization methods to assess their size and stability.

Contribution

It introduces a self-consistent approach to evaluate quantum effects on wormholes with the equation of state p=ωρ, incorporating one-loop graviton contributions and regularization techniques.

Findings

Quantum corrections influence wormhole size depending on ω.

The approach provides a self-consistent method for wormhole stability analysis.

Discussion of phantom energy effects on wormhole properties.

Abstract

We compute the graviton one loop contribution to a classical energy in a \textit{traversable} wormhole background. The form of the shape function considered is obtained by the equation of state $p=\omega\rho$. We investigate the size of the wormhole as a function of the parameter $\omega$. The investigation is evaluated by means of a variational approach with Gaussian trial wave functionals. A zeta function regularization is involved to handle with divergences. A renormalization procedure is introduced and the finite one loop energy is considered as a \textit{self-consistent} source for the traversable wormhole.The case of the phantom region is briefly discussed.