Novel Casimir wormholes in Einstein gravity

TL;DR

This paper explores the possibility of constructing traversable wormholes supported by Casimir energy within Einstein gravity, analyzing various geometric configurations, their energy conditions, stability, and particle trajectories.

Contribution

It introduces new Casimir-supported wormhole solutions with specific shape functions and examines their properties, stability, and physical implications in detail.

Findings

Casimir energy can support traversable wormholes under certain conditions

Wormhole solutions satisfy energy conditions in specific configurations

Stability analysis shows conditions for sustained wormhole structures

Abstract

In the context of General Relativity (GR), violation of the null energy condition (NEC) is necessary for existence of static spherically symmetric wormhole solutions. Also, it is a well-known fact that the energy conditions are violated by certain quantum fields, such as the Casimir effect. The magnitude and sign of the Casimir energy depend on Dirichlet or Neumann boundary conditions and geometrical configuration of the objects involved in a Casimir setup. The Casimir energy may act as an ideal candidate for the matter that supports the wormhole geometry. In the present work, we firstly find traversable wormhole solutions supported by a general form for the Casimir energy density assuming a constant redshift function. As well, in this framework, assuming that the radial pressure and energy density obey a linear equation of state, we derive for the first time Casimir traversable wormhole solutions admitting suitable shape function. Then, we consider three geometric configurations of the Casimir effect such as (i) two parallel plates, (ii) two parallel cylindrical shells, and (iii) two spheres. We study wormhole solutions for each case and their property in detail. We also check the weak and strong energy conditions in the spacetime for the obtained wormhole solutions. The stability of the Casimir traversable wormhole solutions are investigated using the Tolman-Oppenheimer-Volkoff (TOV) equation. Finally, we study trajectory of null as well as timelike particles along with quasi-normal modes (QNMs) of a scalar field in the wormhole spacetime.