Hyperbolic Casimir-like wormhole

TL;DR

This paper explores exact solutions for traversable wormholes in hyperbolic symmetric spacetimes, utilizing negative energy density and a generalized complexity factor to construct Casimir-like wormholes that violate energy conditions.

Contribution

It introduces a novel approach using hyperbolic symmetry and a generalized complexity factor to derive traversable wormholes with negative energy density, replacing exotic matter.

Findings

Wormhole solutions with negative energy density are obtained.

The constructed wormholes violate the null energy condition.

Detailed analysis of matter behavior and traversability conditions.

Abstract

We present a systematic study of exact solutions for traversable wormhole geometries in a static and hyperbolic symmetric spacetime. In the conventional form of studying wormhole geometry, traversability requires the presence of exotic matter, which also provides negative gravity effects to keep the wormhole throat open. Using hyperbolic symmetry we obtain a solution already provided with negative energy density that replaces this effect and allows us to derive wormhole geometries that effectively violate the null energy condition. To achieve this goal, we use a generalized complexity factor for hyperbolic symmetry adapted to study wormhole geometries and with a suitable redshift function in order to construct a Casimir-like traversable hyperbolic wormhole. A detailed study has been conducted on the behavior of the matter sector, the energy conditions, and the traversability conditions.