We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\theta$ ambiguity. We also discuss ambiguities in the Maxwell case, and implication for the loop quantization of these theories.Comment: 5 pages, revtex, no figure

We study the power-law tails in the evolution of massless fields around a fixed background geometry corresponding to a black hole. We give analytical arguments for their existence at scri+, at the future horizon, and at future timelike infinity. We confirm their existence with numerical integrations of the curved spacetime wave equation on the background of a Schwarzschild and a Reissner-Nordstrom black hole. These results are relevant to studies of mass inflation and the instability of Cauchy horizons. The analytic arguments also suggest the behavior of the full nonlinear dynamics, which we study numerically in a companion paper. PACS number(s): 04.30.Db, 04.25.Dm, 04.40.Dg

We study light propagation in the picture of semiclassical space-time that emerges in canonical quantum gravity in the loop representation. In such a picture, where space-time exhibits a polymerlike structure at microscales, it is natural to expect departures from the perfect nondispersiveness of an ordinary vacuum. We evaluate these departures, computing the modifications to Maxwell's equations due to quantum gravity and showing that under certain circumstances nonvanishing corrections appear that depend on the helicity of propagating waves. These effects could lead to observable cosmological predictions of the discrete nature of quantum space-time. In particular, recent observations of nondispersiveness in the spectra of gamma-ray bursts at various energies could be used to constrain the type of semiclassical state that describes the universe.

The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by a common horizon, the problem can be viewed as a perturbation of a single black hole. We take initial data due to Misner for close black holes, apply perturbation theory and evolve the data with the Zerilli equation. The computed gravitational radiation agrees with and extends the results of full numerical computations.

Now in paperback, this text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text begins with a detailed review of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed in detail. Following chapters move on to consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.