Quantum Gravity Hamiltonian for Manifolds with Boundary

In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open Wilson lines in the new variables formulation of quantum gravity. In cases where the boundary conditions fix the metric on the boundary (e.g., in the asymptotically Minkowskian case) one can obtain a finite result, given by a `shift operator' generating translations of the Wilson line in the direction of its tangent vector. A similar shift operator serves as the Hamiltonian constraint in Morales-T\'ecotl and Rovelli's work on quantum gravity coupled to Weyl spinors. This suggests the appearance of an induced field theory of Weyl spinors on the boundary, analogous to that considered in Carlip's work on the statistical mechanics of the 2+1-dimensional black hole.Comment: 17 pages in LaTeX format, vastly improved versio

Matter effects on neutrino oscillations in gravitational and magnetic fields

When neutrinos propagate in a background, their gravitational couplings are modified by their weak interactions with the particles in the background. In a medium that contains electrons but no muons or taons, the matter-induced gravitational couplings of neutrinos are different for the various neutrino flavors, and they must be taken into account in describing the phenomena associated with the neutrino oscillations in the presence of strong gravitational fields. Here we incorporate those couplings in that description, including also the effects of a magnetic field, and consider the implications that they have for the emission of high energy neutrinos in the vicinity of Active Galactic Nuclei.Comment: Latex, 12 page

Critical Behavior of Dimensionally Continued Black Holes

The critical behavior of black holes in even and odd dimensional spacetimes is studied based on Ba\~nados-Teitelboim-Zanelli (BTZ) dimensionally continued black holes. In even dimensions it is found that asymptotically flat and anti de-Sitter Reissner-Nordstr\"om black holes present up to two second order phase transitions. The case of asymptotically anti-de-Sitter Schwarzschild black holes present only one critical transition and a minimum of temperature, which occurs at the transition. Finally, it is shown that phase transitions are absent in odd dimensions.Comment: 21 pages in Latex format, no figures, vastly improved version to appear in Phys. Rev.