Ringholes and closed timelike curves

TL;DR

This paper explores the theoretical possibility of ringholes, a type of spacetime with closed timelike curves, which could potentially serve as time machines without violating classical energy conditions.

Contribution

It introduces the concept of ringholes with specific topological and causal properties, analyzing their classical and quantum stability features.

Findings

Ringholes can form closed timelike curves in multiply connected spacetimes.

Certain regions of ringholes behave like spherical wormholes, while others act as converging lenses.

Angular horizons may prevent quantum instabilities near the throat.

Abstract

It is shown that in a classical spacetime with multiply connected space slices having the topology of a torus, closed timelike curves are also formed. We call these spacetime ringholes. Two regions on the torus surface can be distinguished which are separated by angular horizons. On one of such regions (that which surrounds the maximum circumference of the torus) everything happens like in spherical wormholes, but the other region (the rest of the torus surface), while still possessing a chronology horizon and non-chronal region, behaves like a coverging, rather than diverging, lens and corresponds to an energy density which is always positive for large speeds at or near the throat. It is speculated that a ringhole could be converted into a time machine to perform time travels by an observer who would never encounter any matter that violates the classical averaged weak energy condition. Based on a calculation of vacuum fluctuations, it is also seen that the angular horizons can prevent the emergence of quantum instabilities near the throat.