Dymnikova-Schwinger traversable wormholes

Abstract

In this paper, we obtain new d-dimensional and asymptotically flat wormhole solutions with the presence of determined matter fields in the energy-momentum tensor. This is made by generalizing and adjusting to our purposes the so-called Dymnikova model, originally studied in the context of regular black holes. Thus, we find the constraints of the involved parameters to the formation of those wormholes. Following, we study the properties of such solutions, namely, embedding diagrams, Weak and Null Energy Conditions (WEC and NEC), as well as position-dependent state parameters obeying a linear EoS. We show that the larger the dimension, the larger the flatness of the wormhole and the more pronounced the violation of the energy conditions. We also show that the corresponding fluid behaves as phantom-like in all the space for d ≥ 4. Furthermore, we specialize the employed model for d = 4 spacetime, associating it to the gravitational analogue of the Schwinger effect in a vacuum and correcting the model by introducing a fundamental minimal length via Generalized Uncertainty Principle (GUP). Considering a very small minimal length, we obtain a novel traversable and asymptotically flat wormhole solution. The embedding diagram shows that the presence of that length increases the slope of the wormhole towards its throat compared with the case without it. The correction also attenuates the WEC (and NEC) violations nearby the throat, with the fluid ceasing to be a phantom-type at the Planck scale.