Wormhole geometries supported by three-form fields

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.