Non-exotic traversable wormholes in f (R, TabTab) gravity

In this work we analyze traversable wormhole spacetimes in the framework of a covariant generalization of Einstein's General Relativity known as energy-momentum squared gravity, or f (R, T) gravity, where R is the Ricci scalar, T = TabTab, and T-ab is the energy-momentum tensor. Considering a linear f (R, T) = R + gamma T form, we show that a wide variety of wormhole solutions for which the matter fields satisfy all the energy conditions, namely the null, weak, strong and dominant energy conditions, exist in this framework, without the necessity for a fine-tuning of the free parameters that describe the model. Due to the complexity of the field equations these solutions are obtained through an analytical recursive algorithm. A drawback of the solutions obtained is that they are not naturally localized, and thus a matching with an external vacuum is required. For that purpose, we derive the junction conditions for the theory, and we prove that a matching between two spacetimes must always be smooth, i.e., no thin-shells are allowed at the boundary. Finally, we use these junction conditions to match the interior wormhole spacetime to an exterior vacuum described by the Schwarzschild solution, thus obtaining traversable localized static and spherically symmetric wormhole solutions satisfying all energy conditions for the whole spacetime range. We also prove that the methods outlined in this work can be straightforwardly generalized to more complicated dependencies of the action in T, as long as crossed terms between R and T are absent.

Automated summary

In this work, we analyze traversable wormhole spacetimes within the framework of energy-momentum squared gravity. We show that a wide variety of wormhole solutions satisfying all energy conditions exist without the need for fine-tuning of model parameters. The solutions are obtained through an analytical recursive algorithm, and matching conditions with an external vacuum are derived. By matching the interior wormhole spacetime with the Schwarzschild solution, we obtain localized static and spherically symmetric wormhole solutions that satisfy all energy conditions for the entire spacetime range.