Comments on Microcausality, Chaos, and Gravitational Observables

TL;DR

This paper discusses the nature of gravitational observables, their microcausality properties, and how chaos manifests in black hole spacetimes, highlighting differences between classical and quantum regimes.

Contribution

It proposes that certain classical gravitational observables can satisfy microcausality and explores how this property extends to quantum and semiclassical levels, especially in black hole contexts.

Findings

Classical gravitational observables can satisfy microcausality.

Microcausality may persist at all orders in semiclassical expansion.

Chaos affects black hole observables differently depending on the context.

Abstract

Observables in gravitational systems must be non-local so as to be invariant under diffeomorphism gauge transformations. But at the classical level some such observables can nevertheless satisfy an exact form of microcausality. This property is conjectured to remain true at all orders in the semiclassical expansion, though with limitations at finite $\hbar$ or $\ell_{Planck}$. We also discuss related issues concerning observables in black hole spacetimes and comment on the senses in which they do and do not experience the form of chaos identified by Shenker and Stanford. In particular, in contrast to the situation in a reflecting cavity, this chaos does not afflict observables naturally associated with Hawking radiation for evaporating black holes.