Rotating Rindler-AdS Space

TL;DR

This paper explores stationary vacuum states in three-dimensional anti-de Sitter space, discovering a family of rotating Rindler vacua with observer-dependent horizons and ergospheres, expanding understanding of quantum field theory in curved spacetime.

Contribution

It introduces a new family of rotating Rindler vacua in AdS space, characterized by a rotation parameter, and analyzes their properties and relation to known vacua.

Findings

Existence of rotating Rindler vacua in AdS with non-trivial Bogolubov transformations.

Presence of observer-dependent horizons and ergospheres in these vacua.

Rotating vacua in global AdS require exclusion of certain spacetime regions.

Abstract

If the Hamiltonian of a quantum field theory is taken to be a timelike isometry, the vacuum state remains empty for all time. We search for such stationary vacua in anti-de Sitter space. By considering conjugacy classes of the Lorentz group, we find interesting one-parameter families of stationary vacua in three-dimensional anti-de Sitter space. In particular, there exists a family of rotating Rindler vacua, labeled by the rotation parameter beta, which are related to the usual Rindler vacuum by non-trivial Bogolubov transformations. Rotating Rindler-AdS space possesses not only an observer-dependent event horizon but even an observer-dependent ergosphere. We also find rotating vacua in global AdS provided a certain region of spacetime is excluded.