Date of Award

Spring 2002

Document Type

Restricted Thesis

Terms of Use

© 2002 Kevin Setter. All rights reserved. Access to this work is restricted to users within the Swarthmore College network and may only be used for non-commercial, educational, and research purposes. Sharing with users outside of the Swarthmore College network is expressly prohibited. For all other uses, including reproduction and distribution, please contact the copyright holder.

Degree Name

Bachelor of Arts


Physics & Astronomy Department

First Advisor

Seth Major


This thesis presents an original derivation of the Bekenstein-Hawking formula for the entropy of a black hole within the framework of loop quantum gravity. This derivation differs from preceding ones in that it models the black hole as a grand canonical ensemble and makes use of a recently introduced quasi-local energy operator. It is shown that the statistical mechanics of the model reduces to that of a simple non-interacting gas of distinguishable particles with spin. For temperatures low in comparison with the Planck temperature and boundaries large in comparison with the Planck area, the entropy of the system is shown to be proportional to area (with a logarithmic correction), providing a simple derivation of the Bekenstein-Hawking result (for a certain choice of the Immirzi parameter). Also in this limit, the quantum geometry on the boundary forms a "condensate" in the lowest energy level (j = 1/2). Finally, we relate our description, in terms of the grand canonical ensemble, to previous geometric entropy calculations, which made use of area ensembles.