Nonlocal gravity in a proper tetrad frame: traversable wormholes

TL;DR

This paper explores nonlocal gravity in a tetrad frame to find traversable wormholes, showing nonlocal effects can mimic exotic matter and providing new solutions in modified gravity theories.

Contribution

It introduces a simplified method to solve nonlocal gravity equations in a tetrad frame and constructs new traversable wormhole solutions supported solely by gravity.

Findings

Found new traversable wormhole solutions in nonlocal gravity

Demonstrated nonlocal effects can mimic exotic matter

Provided a step-by-step solution procedure for static, spherically symmetric spacetimes

Abstract

We investigate the revised Deser-Woodard model of nonlocal gravity involving four auxiliary scalar fields, introduced to explain the standard cosmological background expansion history without fine-tuning issues. In particular, we simplify the complex field equations within a proper tetrad frame, thereby recasting the original system into a more tractable equivalent differential problem. We show that, by initially postulating the form of the $g_{tt}$ metric component, it is possible to reconstruct the distortion function of the gravitational model. We then describe a step-by-step procedure for solving the vacuum field equations in the case of a static and spherically symmetric spacetime. We apply our technique to find new traversable wormholes supported purely by gravity by employing either analytical, perturbative, or numerical methods. Furthermore, we demonstrate that the role of the nonlocal effects is analogous to that of exotic matter in general relativity, owing to their quantum nature. Finally, we discuss the main geometric properties of the obtained solutions. Our results present a feasible avenue for identifying novel compact objects while enhancing the comprehension of nonlocal gravitational theories.