TY - JOUR

T1 - Landau-Ginzburg limit of black hole's quantum portrait

T2 - Self-similarity and critical exponent

AU - Dvali, Gia

AU - Gomez, Cesar

N1 - Funding Information:
It is a pleasure to thank Luis Alvarez-Gaumé and Slava Mukhanov for discussions. The work of G.D. was supported in part by Humboldt Foundation under Alexander von Humboldt Professorship , by European Commission under the ERC advanced grant 226371 , by TRR 33 “The Dark Universe” and by the NSF grant PHY-0758032 . The work of C.G. was supported in part by Humboldt Foundation and by Grants: FPA 2009-07908 , CPAN ( CSD2007-00042 ) and HEPHACOS P-ESP00346 .

PY - 2012/9/17

Y1 - 2012/9/17

N2 - 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.

AB - 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.

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U2 - 10.1016/j.physletb.2012.08.019

DO - 10.1016/j.physletb.2012.08.019

M3 - Article

AN - SCOPUS:84865755342

SN - 0370-2693

VL - 716

SP - 240

EP - 242

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1

ER -