Black Hole Entropy and Entropy of Entanglement

TL;DR

This paper compares quantum field corrections to black hole entropy with entanglement entropy, revealing that for certain spins they are identical, but differ due to a contact interaction for spin one.

Contribution

It demonstrates the equivalence of black hole entropy and entanglement entropy for specific fields and identifies a contact interaction responsible for differences in the spin one case.

Findings

Black hole entropy equals entanglement entropy for spin zero and one-half fields.

For spin one fields, a contact interaction causes a discrepancy between the two entropies.

The contact interaction is related to a path integral over particle paths on the horizon.

Abstract

We compare the one-loop corrections to the entropy of a black hole, from quantum fields of spin zero, one-half, and one, to the entropy of entanglement of the fields. For fields of spin zero and one-half the black hole entropy is identical to the entropy of entanglement. For spin one the two entropies differ by a contact interaction with the horizon which appears in the black hole entropy but not in the entropy of entanglement. The contact interaction can be expressed as a path integral over particle paths which begin and end on the horizon; it is the field theory limit of the interaction proposed by Susskind and Uglum which couples a closed string to an open string stranded on the horizon.