Conformally flat traveling plane wave solutions of Einstein equations

We discuss conformally flat plane wave solutions of Einstein equations depending on the plane wave phase [Formula: see text], where [Formula: see text] is the conformal time. We show that ideal fluid Einstein equations and scalar fields with exponential self-interaction have solutions of the form of traveling fluid plane waves. We consider in more detail the source depending on [Formula: see text] with [Formula: see text] describing models of a massless scalar field, electromagnetic field and relativistic particles with space-time depending mass density. We obtain explicit conformally flat metrics solving Einstein equations with a source of the energy–momentum moving with a speed of light.

Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory

We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO(3) Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically nontrivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.

Quantum gravity and renormalization

The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

Asymptotic curvature bounds for conformally flat metrics on the plane

The decay rate of the Gauss curvature of conformally flat planer surfaces of strictly negative curvature is studied. It is show that generically there is an asymptotic sequence that decays faster than quadratically in the distance from the origin. In the case that the conformal factor is of finite order, it is shown that one can improve this decay rate. 2010 Mathematics Subject Classifications. 53C21, 31A05. .