The global rotating scalar field vacuum on anti-de Sitter space-time

TL;DR

This paper investigates the nature of the vacuum state of a quantum scalar field in anti-de Sitter space-time from the perspective of rotating observers, finding that the rotating vacuum coincides with the nonrotating vacuum under certain conditions.

Contribution

It demonstrates that the global rotating vacuum in anti-de Sitter space-time is equivalent to the global nonrotating vacuum, clarifying the role of observer rotation in defining the vacuum state.

Findings

Rotating and nonrotating vacua are identical in anti-de Sitter space.

Positive frequency modes for rotating observers match those of static observers under certain angular velocities.

Implications for constructing global rotating thermal states are discussed.

Abstract

We consider the definition of the global vacuum state of a quantum scalar field on $n$-dimensional anti-de Sitter space-time as seen by an observer rotating about the polar axis. Since positive (or negative) frequency scalar field modes must have positive (or negative) Klein-Gordon norm respectively, we find that the only sensible choice of positive frequency corresponds to positive frequency as seen by a static observer. This means that the global rotating vacuum is identical to the global nonrotating vacuum. For $n\ge 4$, if the angular velocity of the rotating observer is smaller than the inverse of the anti-de Sitter radius of curvature, then modes with positive Klein-Gordon norm also have positive frequency as seen by the rotating observer.We comment on the implications of this result for the construction of global rotating thermal states.