Power-law corrections to entanglement entropy of horizons

TL;DR

This paper investigates how quantum entanglement contributes to black-hole entropy, revealing that superpositions of states introduce power-law corrections to the area law, with implications for understanding horizon thermodynamics.

Contribution

It demonstrates that entanglement entropy of gravitational fluctuation modes includes power-law corrections when the field is in superposition states, extending the traditional area law.

Findings

Entanglement entropy is proportional to horizon area in ground state.

Superpositions introduce fractional power-law corrections to entropy.

Large areas recover the standard area law.

Abstract

We re-examine the idea that the origin of black-hole entropy may lie in the entanglement of quantum fields between inside and outside of the horizon. Motivated by the observation that certain modes of gravitational fluctuations in a black-hole background behave as scalar fields, we compute the entanglement entropy of such a field, by tracing over its degrees of freedom inside a sphere. We show that while this entropy is proportional to the area of the sphere when the field is in its ground state, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. The area law is thus recovered for large areas. Further, we identify location of the degrees of freedom that give rise to the above entropy.