Unimodular Gravity Traversable Wormholes

TL;DR

This paper introduces traversable wormhole solutions within Unimodular Gravity that satisfy traversability conditions while avoiding the need for exotic matter, contrasting with traditional General Relativity wormholes.

Contribution

It presents the first known traversable wormhole solutions in Unimodular Gravity that do not require exotic matter, offering a novel perspective on wormhole physics.

Findings

Wormholes in Unimodular Gravity can be traversable without exotic matter.

The solutions satisfy all metric conditions for traversability.

These wormholes are filled with ordinary matter, unlike in GR.

Abstract

Wormholes are outstanding solutions of Einstein's General Relativity. They were worked out in the late 1980's by Morris and Thorne, who have figured out a recipe that wormholes must obey in order to be traversable, that is, safely crossed by travelers. A remarkable feature is that General Relativity Theory wormholes must be filled by {\it exotic matter}, which Morris and Thorne define as matter satisfying $-p_r>\rho$, in which $p_r$ is the radial pressure and $\rho$ is the energy density of the wormhole. In the present article, we introduce, for the first time in the literature, traversable wormhole solutions of Einstein's Unimodular Gravity Theory. Unimodular Gravity was proposed by Einstein himself as the theory for which the field equations are the traceless portion of General Relativity field equations. Later, Weinberg has shown that this approach elegantly yields the solution of the infamous cosmological constant problem. The wormhole solutions here presented satisfy the metric conditions of "traversability" and remarkably evade the exotic matter condition, so we can affirm that Unimodular Gravity wormholes can be filled by ordinary matter.