Where are the degrees of freedom responsible for black hole entropy?

TL;DR

This paper investigates the spatial origin of degrees of freedom responsible for black hole entropy, showing that near-horizon degrees dominate in ground states, while far-from-horizon degrees become significant in excited states, with implications for understanding black hole thermodynamics.

Contribution

It reveals how the location of degrees of freedom contributing to black hole entropy varies with quantum state, highlighting the role of excited states in entropy corrections.

Findings

Near-horizon degrees dominate in ground state entropy.

Excited states lead to power-law corrections and distant degrees of freedom become significant.

The study clarifies the spatial distribution of entropy-contributing degrees of freedom.

Abstract

Considering the entanglement between quantum field degrees of freedom inside and outside the horizon as a plausible source of black hole entropy, we address the question: {\it where are the degrees of freedom that give rise to this entropy located?} When the field is in ground state, the black hole area law is obeyed and the degrees of freedom near the horizon contribute most to the entropy. However, for excited state, or a superposition of ground state and excited state, power-law corrections to the area law are obtained, and more significant contributions from the degrees of freedom far from the horizon are shown.