An Eternal Time Machine in 2+1 Dimensional anti-de Sitter Space

TL;DR

This paper introduces a new configuration of two orbiting massive point particles in 2+1 dimensional anti-de Sitter space that creates an eternal time machine with closed timelike curves filling the entire space, without horizons.

Contribution

It presents a novel setup of point particles that results in an eternal time machine in anti-de Sitter space, differing from previous solutions by lacking horizons and allowing arbitrary high velocities.

Findings

Eternal time machine configuration with no horizons.

Closed timelike curves fill the entire space.

No lower velocity bound for particles to produce the time machine.

Abstract

2+1 dimensional anti-de Sitter space has been the subject of much recent investigation. Studies of the behaviour of point particles in this space have given us a greater understanding of the BTZ black hole solutions produced by topological identification of adS isometries. In this paper, we present a new configuration of two orbiting massive point particles that leads to an ``eternal'' time machine, where closed timelike curves fill the entire space. In contrast to previous solutions, this configuration has no event or chronology horizons. Another interesting feature is that there is no lower bound on the relative velocities of the point masses used to construct the time machine; as long as the particles exceed a certain mass threshold, an eternal time machine will be produced.