Wormhole Solutions in deformed space-time

TL;DR

This paper explores wormhole solutions within quantized, deformed space-time, analyzing their geometry, traversibility conditions, and the role of exotic matter, particularly Casimir energy, in a non-commutative framework.

Contribution

It constructs and analyzes wormhole solutions in deformed, quantized space-time, revealing that non-commutativity reduces the exotic matter needed for traversibility.

Findings

Non-commutativity reduces the amount of exotic matter required.

Time to traverse the wormhole decreases in non-commutative space-time.

Exotic matter remains necessary for traversibility despite space-time deformation.

Abstract

We construct and analyse wormhole solutions in quantised space-time. The field equations are constructed from the deformed wormhole metric in the proper reference frame using tetrads. The spatial geometry of the wormhole is analysed in the kappa space-time. Further, the modifications to the conditions that ensure traversibility of the wormhole are studied and it is found that the necessity of the exotic matter persists in the non-commuative case as in the commutative space-time. Casimir energy is considered a possible source for exotic matter and it is shown that the time to pass through the wormhole as well as the amount of exotic matter required to create the wormhole reduce due to non-commutativity of space-time.