A Review of Stable, Traversable Wormholes in f (R) Gravity Theories

TL;DR

This review explores stable, traversable wormhole solutions in extended gravity theories, focusing on methods to reduce or eliminate the need for exotic matter through various modified gravity models.

Contribution

It systematically reviews wormhole solutions in extended gravity theories, highlighting approaches to minimize exotic matter requirements compared to standard Einstein gravity.

Findings

Stable wormholes can exist without exotic matter in some extended theories.

Various models like Lovelock and Einstein Dilaton Gauss Bonnet gravity support such solutions.

Alternative techniques reduce the need for exotic matter in wormhole stabilization.

Abstract

It has been proven that in standard Einstein gravity, exotic matter is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field. Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods to minimize the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity, and in this review paper, we first explore modified gravity theories and then explore some wormhole solutions in such theories, including Lovelock gravity and Einstein Dilaton Gauss Bonnet gravity. For completeness, we have also reviewed other wormholes such as Casimir wormholes, dark matter halo wormholes, thin-shell wormholes, and Nonlocal Gravity wormholes, where alternative techniques are used to either avoid or reduce the amount of exotic matter that is required.