Casimir Wormholes in Brans-Dicke Theory

TL;DR

This paper explores static spherically symmetric wormhole solutions in Brans-Dicke gravity supported by Casimir energy, demonstrating conditions under which these wormholes can exist without violating energy conditions and analyzing their stability.

Contribution

It provides the first analysis of Brans-Dicke wormholes supported by Casimir energy, including exact solutions and stability conditions.

Findings

Wormholes can exist without violating energy conditions with repulsive Casimir force.

Exact zero tidal force and non-zero redshift solutions are derived.

Stability analyzed using TOV equation for various parameters.

Abstract

In recent years there has been a growing interest in the field of wormhole physics in the presence of the Casimir effect. As this effect provides negative energy density, it can be utilized as an ideal candidate for the exotic matter required for creating a traversable wormhole. In the context of modified theories of gravity such as Brans-Dicke (BD) theory \cite{BDTH}, wormhole geometries {have} been vastly investigated{. However}, the scientific literature is silent on the issue of BD wormholes in the presence of Casimir energy. Our aim in the present study is to seek for static spherically symmetric solutions representing wormhole configurations in BD theory with Casimir energy as the supporting matter. The Casimir {setup} we assume comprises two electrically neutral, infinitely large parallel planes placed in a vacuum. We then consider the Casimir vacuum energy density of a scalar field in such a configuration with Dirichlet {and} mixed boundary conditions. In the former case, the corresponding Casimir force is attractive and in the latter this force is repulsive. We present exact zero tidal force wormhole solutions as well as those with non-vanishing redshift function for both types of Casimir energies. The conditions on wormhole solutions along with the weak (WEC) and null (NEC) energy conditions put constraints on the values of BD coupling parameter. These constraints are also subject to the value of BD scalar field at the throat and the throat radius. We therefore find that BD wormholes in the presence of Casimir energy can exist without violating NEC and WEC (for the repulsive Casimir force). Finally, we examine the equilibrium condition for the stability of the obtained solutions using Tolman-Oppenheimer-Volkoff (TOV) equation.