Chronology protection in Gödel-type universes via quantum backreaction

Develop a quantum field–theoretic formulation of the angular momentum generator J in Gödel-type universes and analyze the backreaction of vacuum fluctuations on the spacetime metric to properly address Hawking’s chronology protection conjecture in these spacetimes.

Background

The paper studies the internal quantum statistical mechanics of a thermally isolated spaceship traveling along a closed timelike curve (CTC) in axisymmetric spacetimes, using Wigner’s theorem and the symmetry generated by rotations to show that the Hamiltonian spectrum becomes discretized and histories are self-consistent. This analysis is performed on a fixed classical spacetime background without considering the backreaction of quantum fields.

In the conclusions, the authors note that fully addressing whether chronology protection forbids CTCs in Gödel-type universes requires going beyond their scope: specifically, one must express the symmetry generator J in terms of quantum fields and evaluate the backreaction of vacuum fluctuations on the spacetime metric. This identifies a concrete unresolved task directly tied to assessing the chronology protection conjecture in these geometries.

References

In fact, a proper discussion of the chronology protection conjecture [41, 42] in Gödel-type universes would require that we express the operator J (defined in section II B) in terms of quantum fields, and that we study the backre- action of the vacuum fluctuations on the spacetime met- ric [43-45], which is beyond the scope of this article5.

— Life on a closed timelike curve  (2405.18640 - Gavassino, 2024) in Section V (Conclusions)

The existence of CTCs in mathematically consistent solutions raises a significant question as to whether it is possible for such causality violating regions to exist in physically relevant spacetimes, or is there a physical mechanism that prevents their formation. This question is closely related to Hawking's chronology protection conjecture , according to which the physical effects associated with the formation of a chronology horizon may prevent CTCs from appearing. This possibility has also been studied from the perspective of quantum field theory in curved spacetime . However, a general proof of the mechanism remains unknown.

— Closed timelike curves in modified theories of gravity  (2610.01476 - Roy et al., 1 Oct 2026) in Section 1, Introduction