Eternal time machine in $\mathrm{}(2+1)\mathrm{}$-dimensional anti–de Sitter space

$\mathrm{}(2+1)\mathrm{}$-dimensional anti–de Sitter space has been the subject of much recent investigation. Studies of the behavior 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 with 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.