Quantum Hairs and Isolated Horizon Entropy from Chern-Simons Theory
Year: 2013
Type: preprint
Abstract: We articulate the fact that the loop quantum gravity description of the quantum macrostates of black hole horizons, modeled as Quantum Isolated Horizons (QIHs), is completely characterized in terms of two independent integer-valued ‘quantum hairs’, viz,. the coupling constant of the quantum SU(2) Chern-Simons theory describing QIH dynamics, and the number of punctures produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the ChernSimons fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this Chern-Simons theory, using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semiclassical input from general relativity vis-a-vis the functional dependence of the IH mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein-Hawking area law relates these two parameters (as an equilibrium ‘equation of state’) and consequently imposes restrictions on the allowed values of the Barbero-Immirzi parameter. The logarithmic correction to the area law obtained a decade ago by R. Kaul and one of us (P.M.), ensues straightforwardly, with precisely the coefficient -3/2, making it a signature of the loop quantum gravity approach to black hole entropy.
Source: arXiv (Cornell University)
Authors: Abhishek Majhi, Parthasarathi Majumdar
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2735518379