Ground state energy in a wormhole space-time

TL;DR

This paper calculates the ground state energy of a scalar field in a wormhole spacetime using zeta renormalization, identifying conditions for stable wormhole configurations and their physical parameters.

Contribution

It provides a detailed calculation of the ground state energy in a wormhole background and determines stability conditions based on the scalar field coupling parameter.

Findings

Stable wormholes exist for coupling b3 > 0.123

For conformal coupling b3=1/6, the throat radius is approximately 0.16/m

Self-consistent wormholes have a throat radius around 0.0141 times the Planck length

Abstract

The ground state energy of the massive scalar field with non-conformal coupling $\xi$ on the short-throat flat-space wormhole background is calculated by using zeta renormalization approach. We discuss the renormalization and relevant heat kernel coefficients in detail. We show that the stable configuration of wormholes can exist for $\xi > 0.123$. In particular case of massive conformal scalar field with $\xi=1/6$, the radius of throat of stable wormhole $a\approx 0.16/m$. The self-consistent wormhole has radius of throat $a\approx 0.0141 l_p $ and mass of scalar boson $m\approx 11.35 m_p$ ($l_p$ and $m_p$ are the Planck length and mass, respectively).