Wormhole geometries supported by three-form fields

TL;DR

This paper explores novel wormhole solutions supported by three-form fields, demonstrating that such fields can sustain wormholes without violating energy conditions, and may behave like a cosmological constant under certain conditions.

Contribution

It introduces new static, spherically symmetric wormhole geometries supported by three-form fields, showing they can satisfy energy conditions and differ from standard General Relativity solutions.

Findings

Matter fields can satisfy energy conditions with three-form support.

Three-form fields can mimic a cosmological constant.

Wormholes are supported without exotic matter.

Abstract

In this work, we find novel static and spherically symmetric wormhole geometries using a three-form field. By solving the gravitational field equations, we find a variety of analytical and numerical solutions and show that it is possible for the matter fields threading the wormhole to satisfy the null and weak energy conditions throughout the spacetime, when the three-form field is present. In these cases, the form field is responsible for supporting the wormhole and all the exoticity is confined to it. Thus, the three-form curvature terms, which may be interpreted as a gravitational fluid, sustain these non-standard wormhole geometries, fundamentally different from their counterparts in General Relativity. We also show that in the case of a vanishing redshift function the field can display a cosmological constant behavior.