No Time Machines from Lightlike Sources in 2+1 Gravity

TL;DR

This paper investigates the formation of closed timelike curves in 2+1 gravity with lightlike sources, showing they are only possible under unphysical conditions and are forbidden in topologically massive gravity.

Contribution

It extends previous work to lightlike sources, demonstrating the presence or absence of CTCs and the role of topologically massive gravity in forbidding them.

Findings

CTCs appear at spatial infinity if present at all.

CTCs are forbidden in topologically massive gravity with lightlike sources.

Energy surpassing the tachyonic bound leads to CTC formation at infinity.

Abstract

We extend the argument that spacetimes generated by two timelike particles in D=3 gravity (or equivalently by parallel-moving cosmic strings in D=4) permit closed timelike curves (CTC) only at the price of Misner identifications that correspond to unphysical boundary conditions at spatial infinity and to a tachyonic center of mass. Here we analyze geometries one or both of whose sources are lightlike. We make manifest both the presence of CTC at spatial infinity if they are present at all, and the tachyonic character of the system: As the total energy surpasses its tachyonic bound, CTC first begin to form at spatial infinity, then spread to the interior as the energy increases further. We then show that, in contrast, CTC are entirely forbidden in topologically massive gravity for geometries generated by lightlike sources.