Energy-Momentum Restrictions on the Creation of Gott Time Machines

TL;DR

This paper investigates the conditions under which Gott time machines, involving closed timelike curves, can form in an open universe within (2+1)-dimensional gravity, concluding that energy constraints prevent their formation.

Contribution

It introduces a new method to analyze momentum inequalities in (2+1)-dimensional gravity and demonstrates that energy restrictions prevent Gott-like time machines in open universes.

Findings

No sufficient energy to accelerate particles for time machine creation.

Energy constraints enforce no-CTC theorems in open universes.

Develops a simple approach to momentum inequalities in (2+1)D gravity.

Abstract

The discovery by Gott of a remarkably simple spacetime with closed timelike curves (CTC's) provides a tool for investigating how the creation of time machines is prevented in classical general relativity. The Gott spacetime contains two infinitely long, parallel cosmic strings, which can equivalently be viewed as point masses in (2+1)-dimensional gravity. We examine the possibility of building such a time machine in an open universe. Specifically, we consider initial data specified on an edgeless, noncompact, spacelike hypersurface, for which the total momentum is timelike (i.e., not the momentum of a Gott spacetime). In contrast to the case of a closed universe (in which Gott pairs, although not CTC's, can be produced from the decay of stationary particles), we find that there is never enough energy for a Gott-like time machine to evolve from the specified data; it is impossible to accelerate two particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism different from that which operates in a closed universe. In proving our result, we develop a simple method to understand the inequalities that restrict the result of combining momenta in (2+1)-dimensional gravity.