Dirac fermion, cosmological event horizons and quantum entanglement

TL;DR

This paper investigates the quantum entanglement of Dirac fermions in de Sitter spacetime, calculating entanglement entropy between causally disconnected regions and exploring its dependence on spacetime parameters.

Contribution

It introduces a method for quantising Dirac fermions in de Sitter space and computes the entanglement entropy, extending the analysis to Kerr-de Sitter spacetime and black hole horizons.

Findings

Entanglement entropy depends on spacetime parameters and eigenvalues.

Numerical analysis shows how entropy varies with different spacetime configurations.

The approach can be extended to other static and stationary spacetimes.

Abstract

We discuss the field quantisation of a free massive Dirac fermion in the two causally disconnected static patches of the de Sitter spacetime, by using mode functions that are normalisable on the cosmological event horizon. Using this, we compute the entanglement entropy of the vacuum state corresponding to these two regions, for a given fermionic mode. Further extensions of this result to more general static spherically symmetric and stationary axisymmetric spacetimes are discussed. For the stationary axisymmetric Kerr-de Sitter spacetime in particular, the variations of the entanglement entropy with respect to various eigenvalues and spacetime parameters are depicted numerically. We also comment on such variations when instead we consider the non-extremal black hole event horizon of the same spacetime.