The boundary of G\"odel's spacetime and the chronology protection conjecture

TL;DR

This paper constructs a specific spacetime model in three-dimensional gravity that supports Hawking's chronology protection conjecture, showing causality violations are hidden behind a Cauchy surface, thus preserving causality.

Contribution

It introduces a homogeneous anisotropic conformal spacetime with a novel symmetry group that demonstrates causality violations can be concealed within a Cauchy surface, supporting the chronology protection conjecture.

Findings

Causality violations are hidden behind a Cauchy spacelike surface.

The spacetime admits positive mass, momentum, and angular momentum.

The model is based on the automorphism group of the Heisenberg motion group.

Abstract

We present a homogenous anisotropic conformal spacetime manifold that provide an example of Hawking's chronology protection conjecture in three-dimensional gravity theory. The solution is based upon the fact that the seven-dimensional group of the automorphism of the Heisenberg motion group H1{\times}U(1), modulo discrete sub-group \Gamma, is the symmetry group of the sub-Riemannian (SR)- manifold, boundary of the Cauchy-Riemann (CR)-manifold, allowing the existence of positive mass, momentum, angular-momentum and timelike-translation. It is shown that many mirror symmetric self-similar G\"odel's surfaces are hidden behind a Cauchy spacelike surface so that causality violation is not visible from outside.