Gravitational statistical mechanics: a model
Abstract
Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for Lorentzian general relativity. In this model, states of quantum geometry are represented by spin networks. We show that the statistical mechanics of the model reduces to that of a simple noninteracting gas of particles with spin. Using both canonical and grand canonical descriptions, we investigate two temperature regimes determined by the fundamental constant in the theory, m. In the high temperature limit (kT > m), the model is thermodynamically stable. For low temperatures (kT < m) and for macroscopic areas of the bounding surface, the entropy is proportional to area (with logarithmic correction), providing a simple derivation of the BekensteinHawking result. By comparing our results to known semiclassical relations we are able to fix the fundamental scale. Also in the low temperature, macroscopic limit, the quantum geometry on the boundary forms a `condensate' in the lowest energy level (j=1/2).
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2001
 DOI:
 10.1088/02649381/18/23/309
 arXiv:
 arXiv:grqc/0101031
 Bibcode:
 2001CQGra..18.5125M
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 19 pages, 1 figure