Quantum versions of Carlini-Miji\'c wormholes

TL;DR

This paper explores quantum wormholes derived from classical models by Carlini and Mijić, demonstrating their consistency with the Hawking-Page conjecture and extending the analysis to cases violating the strong energy condition.

Contribution

It introduces simplified Wheeler-DeWitt equations for quantum wormholes and shows their existence under both strong energy condition satisfaction and violation.

Findings

Quantum wormholes are consistent with the Hawking-Page conjecture.

Wormholes exist even when the strong energy condition is violated.

Results support the generality of wormhole solutions in the Wheeler-DeWitt framework.

Abstract

We consider the quantum analogues of wormholes obtained by Carlini and Miji\'c (CM), who analytically continued closed universe models. To obtain wormholes when the strong energy condition ($\gamma>2/3$) is satisfied, we are able to simplify the Wheeler-DeWitt (WDW) equation by using an equivalent scalar potential which is a function of the scale factor. Such wormholes are found to be consistent with the Hawking-Page (HP) conjecture for quantum wormholes as solutions of the WDW equation. In addition to the CM type wormholes, for a scalar field realization of the potential in the WDW equation we also obtain quantum wormholes when the strong energy condition is violated. This violation can be up to an arbitrary large distance from the wormhole throat, before the violation eventually has to be relaxed in order to have a flat Euclidean space time. These results give support to the claim of HP that wormhole solutions are a fairly general property of the WDW equation. However, by allowing such solutions one might be precluding other more important properties such as a Lorentzian behaviour and a possible inflationary earlier stage of our universe.