Corrections in the relative entropy of black hole microstates

TL;DR

This paper investigates how the distinguishability of black hole microstates from thermal states, measured by relative entropy, varies with region size and microstate properties, revealing nonzero entropy in certain cases.

Contribution

It demonstrates that vacuum block dominance assumptions fail for some microstates, leading to nonzero relative entropy even in small regions, advancing understanding of black hole microstate distinguishability.

Findings

Average relative entropy vanishes for small regions under vacuum block dominance.

Vacuum block dominance failure causes nonzero entropy in some microstates.

Microstate distinguishability depends on specific properties of the BTZ black hole microstates.

Abstract

Inspired by the recent work of Bao and Ooguri (BO), we study the distinguishability of the black hole microstates from the thermal state as captured by the average of their relative entropies: the Holevo information. Under the assumption that the vacuum conformal block dominates the entropy calculation, BO find that the average relative entropy vanishes on spatial regions less than half the size of the CFT. However, vacuum block dominance fails for some microstates of the $M=0$ BTZ black hole. We show that this renders the average relative entropy nonzero even on infinitesimal intervals at $O(c^0)$.