Unitarity in the Presence of Closed Timelike Curves

TL;DR

This paper explores the conditions under which quantum dynamics remain consistent in spacetimes with closed timelike curves, specifically analyzing BTZ black holes and demonstrating unitarity preservation at certain discrete gravitational couplings.

Contribution

It shows that, despite perturbative unitarity failure, unitarity can be restored in certain cases by analyzing physics inside the horizon and near the singularity, linking to dual CFT predictions.

Findings

Unitarity is preserved at discrete gravitational couplings.

Quantization of black hole angular momentum is consistent with dual CFT.

Analysis is performed at low energies, ignoring string effects.

Abstract

We conjecture that, in certain cases, quantum dynamics is consistent in the presence of closed timelike curves. We consider time dependent orbifolds of three dimensional Minkowski space describing, in the limit of large AdS radius, BTZ black holes inside the horizon. Although perturbative unitarity fails, we show that, for discrete values of the gravitational coupling, particle propagation is consistent with unitarity. This quantization corresponds to the quantization of the black hole angular momentum, as expected from the dual CFT description. Note, however, that we recover this result by analyzing the physics inside the horizon and near the singularity. The spacetime under consideration has no AdS boundary, and we are therefore not using any assumption regarding a possible dual formulation. We perform the computation at very low energies, where string effects are irrelevant and interactions are dominated by graviton exchange in the eikonal regime. We probe the non-causal structure of space-time to leading order, but work to all orders in the gravitational coupling.