Wave propagation on a random lattice

Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic lattice. We use this to calculate the lowest order coefficients of the dispersion relation for a specific one-dimensional model.Comment: 13 pages, 3 figures. v3: Some minor changes and clarifications. Virtually identical with the version published in Physical Review

From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity

We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization of vacuum general relativity in loop quantum gravity.Comment: 56 pages. Contribution to the Proceedings of the 3rd Quantum Geometry and Quantum Gravity School in Zakopane (2011). v2: Typos corrected, various small changes in presentation, version as published in Po

Toward explaining black hole entropy quantization in loop quantum gravity

In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this step-like behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step-length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking.Comment: 15 pages, 5 figures. v3: final version (essentially as it appeared in PRD