Wormhole geometries in $f\left(R,T^2\right)$ gravity satisfying the energy conditions

TL;DR

This paper investigates traversable wormholes in $f(R,T^2)$ gravity, demonstrating the existence of solutions satisfying all energy conditions without fine-tuning, and establishing junction conditions for localized, physically viable wormholes.

Contribution

It introduces a method to construct energy-condition-satisfying wormholes in $f(R,T^2)$ gravity and derives junction conditions for their localization.

Findings

Existence of wormhole solutions satisfying all energy conditions.

Smooth junction conditions prevent thin shells at the interface.

Method applicable to more complex $T^2$ dependencies.

Abstract

We explore the properties of traversable wormhole spacetimes within the framework of energy-momentum squared gravity, also known as $f(R,T^2)$ gravity, where $R$ represents the Ricci scalar, $T_{ab}$ is the energy-momentum tensor, and $T^2 = T_{ab}T^{ab}$. Adopting a linear functional form $f(R,T^2) = R + \gamma T^2$, we demonstrate the existence of a wide range of wormhole solutions that satisfy all of the energy conditions without requiring fine-tuning of the model parameters. Due to the inherent complexity of the field equations, these solutions are constructed through an analytical recursive method. However, they lack a natural localization, requiring a junction with an external vacuum region. To address this, we derive the corresponding junction conditions and establish that the matching must always be smooth, precluding the formation of thin shells at the interface. Using these conditions, we match the interior wormhole geometry to an exterior Schwarzschild solution, yielding localized, static, and spherically symmetric wormholes that satisfy all the energy conditions throughout the entire spacetime. Finally, we extend our analysis to more intricate dependencies on $T^2$, demonstrating that the methodology remains applicable as long as no mixed terms between $R$ and $T^2$ are introduced.