Landau-Ginzburg Limit of Black Hole's Quantum Portrait: Self Similarity and Critical Exponent

TL;DR

This paper models black holes as Bose condensates of gravitons, deriving a Landau-Ginzburg description that captures their semi-classical properties and reveals a critical scaling law with exponent 1/3.

Contribution

It introduces a Landau-Ginzburg effective theory for black hole quantum states, linking graviton condensates to phase transition concepts and deriving a critical exponent for black hole scaling.

Findings

Landau-Ginzburg Lagrangian describes black hole condensates.

Hawking radiation corresponds to slow-roll depletion of N.

Scaling law with critical exponent 1/3 for black hole size.

Abstract

Recently we have suggested that the microscopic quantum description of a black hole is an overpacked self-sustained Bose-condensate of N weakly-interacting soft gravitons, which obeys the rules of 't Hooft's large-N physics. In this note we derive an effective Landau-Ginzburg Lagrangian for the condensate and show that it becomes an exact description in a semi-classical limit that serves as the black hole analog of 't Hooft's planar limit. The role of a weakly-coupled Landau-Ginzburg order parameter is played by N. This description consistently reproduces the known properties of black holes in semi-classical limit. Hawking radiation, as the quantum depletion of the condensate, is described by the slow-roll of the field N. In the semiclassical limit, where black holes of arbitrarily small size are allowed, the equation of depletion is self similar leading to a scaling law for the black hole size with critical exponent 1/3.