Monsters, black holes and the statistical mechanics of gravity

TL;DR

This paper reviews the concept of 'monsters' in classical general relativity, objects with finite mass and area but potentially unbounded entropy, and explores how high-dimensional Hilbert space properties could underpin a statistical mechanics framework for gravity.

Contribution

It introduces the notion of gravitational monsters with high entropy and discusses how recent Hilbert space geometry results could inform a statistical mechanics approach to gravity.

Findings

Monsters can have more entropy than black holes of equal mass.

High-dimensional Hilbert space geometry offers insights into gravitational statistical mechanics.

Monsters challenge traditional interpretations of black hole entropy and dualities.

Abstract

We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is the curvature or energy density required to be large in Planck units, and quantum gravitational effects are, in the conventional effective field theory framework, small everywhere. Since they can have more entropy than a black hole of equal mass, monsters are problematic for certain interpretations of black hole entropy and the AdS/CFT duality. In the second part of the paper we review recent developments in the foundations of statistical mechanics which make use of properties of high-dimensional (Hilbert) spaces. These results primarily depend on kinematics -- essentially, the geometry of Hilbert space -- and are relatively insensitive to dynamics. We discuss how this approach might be adopted as a basis for the statistical mechanics of gravity. Interestingly, monsters and other highly entropic configurations play an important role.