Black Hole Interior in Unitary Gauge Construction

TL;DR

This paper explores a unitary gauge approach to black hole interiors, showing how interior operators emerge from collective degrees of freedom and analyzing their state dependence and errors within a finite-dimensional effective theory.

Contribution

It introduces a novel unitary gauge construction for black hole interiors, explicitly constructing interior operators without microscopic details and analyzing their state dependence and associated errors.

Findings

Interior operators can be constructed without microscopic details.

There is an intrinsic ambiguity in semiclassical theory with finite degrees of freedom.

A connection to quantum error correction in holography is discussed.

Abstract

A quantum system with a black hole accommodates two widely different, though physically equivalent, descriptions. In one description, based on global spacetime of general relativity, the existence of the interior region is manifest, while understanding unitarity requires nonperturbative quantum gravity effects such as replica wormholes. The other description adopts a manifestly unitary, or holographic, description, in which the interior emerges effectively as a collective phenomenon of fundamental degrees of freedom. In this paper we study the latter approach, which we refer to as the unitary gauge construction. In this picture, the formation of a black hole is signaled by the emergence of a surface (stretched horizon) possessing special dynamical properties: quantum chaos, fast scrambling, and low energy universality. These properties allow for constructing interior operators, as we do explicitly, without relying on details of microscopic physics. A key role is played by certain coarse modes in the zone region (hard modes), which determine the degrees of freedom relevant for the emergence of the interior. We study how the interior operators can or cannot be extended in the space of microstates and analyze irreducible errors associated with such extension. This reveals an intrinsic ambiguity of semiclassical theory formulated with a finite number of degrees of freedom. We provide an explicit prescription of calculating interior correlators in the effective theory, which describes only a finite region of spacetime. We study the issue of state dependence of interior operators in detail and discuss a connection of the resulting picture with the quantum error correction interpretation of holography.