The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon

TL;DR

This paper calculates the fermionic entanglement entropy of the vacuum state at a Schwarzschild black hole horizon, revealing how quantum entanglement relates to black hole horizon properties.

Contribution

It introduces a method to compute fermionic entanglement entropy for black hole horizons using separation of variables and Dirac propagator integral representations.

Findings

Entanglement entropy is proportional to the number of occupied angular momentum modes.

The approach provides a quantitative link between quantum entanglement and black hole horizon characteristics.

The method can be applied to analyze quantum fields in curved spacetime environments.

Abstract

We define and analyze the fermionic entanglement entropy of a Schwarzschild black hole horizon for the regularized vacuum state of an observer at infinity. Using separation of variables and an integral representation of the Dirac propagator, the entanglement entropy is computed to be a prefactor times the number of occupied angular momentum modes on the event horizon.