Overcounting of interior excitations: A resolution to the bags of gold paradox in AdS

TL;DR

This paper resolves the paradox of seemingly excessive interior excitations in AdS black holes by showing they have small inner products, allowing a large number of excitations without violating entropy or spectral properties, with validation in toy models.

Contribution

It introduces a resolution to the bags of gold paradox by demonstrating small inner products between excitations, reconciling semiclassical bulk excitations with dual CFT descriptions.

Findings

No paradox in dual CFT description.

Small inner products enable large number of excitations.

Validation in toy matrix models.

Abstract

In this work, we investigate how single-sided and eternal black holes in AdS can host an enormous number of semiclassical excitations in their interior, which is seemingly not reflected in the Bekenstein Hawking entropy. In addition to the paradox in the entropy, we argue that the treatment of such excitations using effective field theory also violates black holes' expected spectral properties. We propose that these mysteries are resolved because apparently orthogonal semiclassical bulk excitations have small inner products between them; and consequently, a vast number of semiclassical excitations can be constructed using the Hilbert space which describes black hole's interior. We show that there is no paradox in the dual CFT description and comment upon the initial bulk state, which leads to the paradox. Further, we demonstrate our proposed resolution in the context of small $N$ toy matrix models, where we model the construction of these large number of excitations. We conclude by discussing why this resolution is special to black holes.