Entanglement of the Vacuum between Left, Right, Future, and Past: Dirac spinor in Rindler spaces and Kasner spaces

TL;DR

This paper explores the entanglement structure of the Minkowski vacuum for Dirac fields across Rindler and Kasner spacetimes, providing explicit mode relations and vacuum state descriptions.

Contribution

It introduces a unified analytical framework connecting Dirac mode functions in Rindler and Kasner coordinates, revealing vacuum entanglement in these spacetimes.

Findings

Explicit form of Minkowski vacuum in Kasner and Rindler regions

Unified mode function correspondence between regions

Demonstration of vacuum entanglement across spacetime regions

Abstract

We study the relations of the positive frequency mode functions of Dirac field in 4-dimensional Minkowski spacetime covered with Rindler and Kasner coordinates, and describe the explicit form of the Minkowski vacuum state with the quantum states in Kasner and Rindler regions, and analytically continue the solutions. As a result, we obtain the correspondence of the positive frequency mode functions in Kasner region and Rindler region in a unified manner which derives vacuum entanglement.