The Library of Babel: On the origin of gravitational thermodynamics

TL;DR

This work argues that heavy pure states of gravity, including AdS5 Schwarzschild black holes, appear mixed to almost all probes due to statistical typicality of underlying microstates. By leveraging AdS/CFT and information-theoretic notions, the authors show that correlation functions of typical heavy operators are universal except for exponentially small corrections, leading to an emergent thermodynamic description of gravity. The half-BPS sector is exploited as an exactly tractable arena where microstates map to free-fermion configurations and limit shapes; from this, a foam-like microscopic structure with effective singular geometries (hyperstar and superstar) emerges as the universal low-energy description. The paper argues that such a foam-driven, coarse-grained gravity explains the thermodynamic character of black holes without violating unitarity, and discusses broader implications for correlation functions, horizons, and extensions beyond supersymmetry.

Abstract

We show that heavy pure states of gravity can appear to be mixed states to almost all probes. For AdS_5 Schwarzschild black holes, our arguments are made using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For half-BPS states of the theory which are incipient black holes, our account is exact: typical microstates are described in gravity by a spacetime ``foam'', the precise details of which are almost invisible to almost all probes. We show that universal low-energy effective description of a foam of given global charges is via certain singular spacetime geometries. When one of the specified charges is the number of D-branes, the effective singular geometry is the half-BPS ``superstar''. We propose this as the general mechanism by which the effective thermodynamic character of gravity emerges.

Figures (6)

• Figure 1: The Wigner distribution function of a single fermion with excitation level $n=50$ as a function of $H/\hbar$.
• Figure 2: The sum of Wigner distribution functions of single fermions with excitation levels between $n=200$ and $n=300$ as a function of $H/\hbar$.
• Figure 3: The sum of Wigner distribution functions of single fermions with excitation levels between $n=200$ and $n=300$ separated by steps $\delta=2$ as a function of $H/\hbar$.
• Figure 4: The Husimi distribution function of a single fermion with excitation level $n=50$ as a function of $H/\hbar$. Compare with figure \ref{['fig:wigner']}.
• Figure 5: The sum of Husimi distribution functions of single fermions with excitation levels between $n=200$ and $n=300$ as a function of $H/\hbar$. Compare with figure \ref{['fig:wignersumI']}.