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 Letter 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 semi-classical 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 13.
|Original language||English (US)|
|Number of pages||3|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - Sep 17 2012|
ASJC Scopus subject areas
- Nuclear and High Energy Physics