2012/08/16 by Deepak Vaid, Vaid, Deepak
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1208.3335
24 pages, 7 figures; comments welcome
arxiv created 2012/08/16 · openalex publication_date 2012/08/16 · arxiv updated 2012/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In LQG, black hole horizons are described by 2+1 dimensional boundaries of a bulk 3+1 dimensional spacetime. The horizon is endowed with area by lines of gravitational flux which pierce the surface. As is well known, counting of the possible states associated with a given set of punctures allows us to recover the famous Bekenstein-Hawking area law according to which the entropy of a black hole is proportional to the area of the associated horizon SBH ∝ AHor . It is also known that the dynamics of the horizon degrees of freedom is described by the Chern-Simons action of a \mathfraksu(2) (or \mathfraku(1) after a certain gauge fixing) valued gauge field Aμi. Recent numerical work which performs the state-counting for punctures, from first-principles, reveals a step-like structure in the entropy-area relation. We argue that both the presence of the Chern-Simons action and the step-like structure in the entropy-area curve are indicative of the fact that the effective theory which describes the dynamics of punctures on the horizon is that of the Quantum Hall Effect.