Formation of closed timelike curves in a composite vacuum/dust asymptotically-flat spacetime

TL;DR

This paper introduces a new asymptotically-flat spacetime model composed of vacuum and dust that evolves from a regular initial state to develop closed timelike curves, satisfying energy conditions and having a well-posed initial-value problem.

Contribution

It presents a novel vacuum/dust spacetime model that forms closed timelike curves from regular initial data while satisfying all energy conditions and maintaining a well-posed evolution.

Findings

Closed timelike curves form in a compact region.

The model satisfies all standard energy conditions.

The spacetime evolution is governed by a well-posed initial-value problem.

Abstract

We present a new asymptotically-flat time-machine model made solely of vacuum and dust. The spacetime evolves from a regular spacelike initial hypersurface S and subsequently develops closed timelike curves. The initial hypersurface S is asymptotically flat and topologically trivial. The chronology violation occurs in a compact manner; namely the first closed causal curves form at the boundary of the future domain of dependence of a compact region in S (the core). This central core is empty, and so is the external asymptotically flat region. The intermediate region surrounding the core (the envelope) is made of dust with positive energy density. This model trivially satisfies the weak, dominant, and strong energy conditions. Furthermore it is governed by a well-defined system of field equations which possesses a well-posed initial-value problem.