Dymnikova-Schwinger traversable wormholes

TL;DR

This paper constructs new higher-dimensional asymptotically flat traversable wormhole solutions based on a generalized Dymnikova model, analyzing their properties, energy conditions, and effects of a minimal length correction inspired by quantum gravity.

Contribution

It introduces a novel class of $d$-dimensional wormholes using a generalized Dymnikova energy density, including a minimal length correction that influences energy condition violations.

Findings

Larger dimensions lead to more flat wormholes and increased energy condition violations.

The fluid near the throat behaves as phantom-like for $d \,\geq\, 4$.

Minimal length correction reduces WEC and NEC violations, making the fluid non-phantom at the Planck scale.

Abstract

In this paper, we obtain new $d$-dimensional and asymptotically flat wormhole solutions by assuming a specific form of the energy density distribution. This is addressed by considering the generalization of the so-called Dymnikova model, originally studied in the context of regular black holes. In this way, we find constraints for the involved parameters, namely, the throat radius, the scale associated to the matter distribution, and the spacetime dimension, to build those wormholes. Following, we study the properties of the obtained solutions, namely, embedding diagrams as well as Weak and Null Energy Conditions (WEC and NEC). We show that the larger the dimension, the larger the flatness of the wormhole and the more pronounced the violation of these energy conditions. We also show that the corresponding fluid behaves as phantom-like for $d \geq 4$ in the neighborhood of the wormhole throat. In addition, we specialize the employed model for $d=4$ spacetime, associating it with the gravitational analog of the Schwinger effect in a vacuum and correcting the model by introducing a minimal length via Generalized Uncertainty Principle (GUP). Thus, we obtain a novel traversable and asymptotically flat wormhole solution by considering that the minimal length is very tiny. The associated embedding diagram shows us that the presence of this fundamental quantity increases the slope of the wormhole towards its throat compared with the case without it. That correction also attenuates the WEC (and NEC) violations nearby the throat, with the fluid ceasing to be a phantom-type at the Planck scale, unlike the case without the minimal length.