Conformal geometry of gravitational plane waves
نویسنده
چکیده
It is well known that the conformal group of a non-flat vacuum pp-wave is at most 7-dimensional. Here we explicitly determine all solutions with a 7-dimensional group in three particular families of gravitational plane waves. All of them are exact solutions in terms of elementary functions. Furthermore, it turns out that a gravitational plane wave with a 6-dimensional homothety group (larger than the isometry group) does not have to be real analytic. It may contain an open flat part even if it is not conformally flat. Finally we classify all vacuum pp-waves admitting a particular standard conformal vector field arising from flat Minkowski space. 2000 MSC classification: 53B30, 53C50, 83C20
منابع مشابه
ar X iv : h ep - t h / 06 02 12 8 v 1 1 3 Fe b 20 06 Strings in plane - fronted gravitational waves
Brinkmann's plane-fronted gravitational waves with parallel rays — shortly pp-waves — are shown to provide, under suitable conditions, exact string vacua at all orders of the sigma-model perturbation expansion. 1. Introduction The condition for the vanishing of the conformal anomaly for a bosonic string in a curved space is expressed, in σ-model perturbation theory, as R µν +. .. = 0, where the...
متن کاملRefractive Gravitational Waves and Quantum Fluctuations
Refractive gravitational waves are a generalisation of impulsive waves on a null hypersurface in which the metric is discontinuous but a weaker continuity condition for areas holds. A simple example of a plane wave is examined in detail and two arguments are given that this should be considered a solution of Einstein’s vacuum field equations. The study of these waves is motivated by quantum gra...
متن کاملOn the geometry of impulsive gravitational waves
We describe impulsive gravitational pp-waves entirely in the distributional picture. Applying Colombeau’s nonlinear framework of generalized functions we handle the formally ill-defined products of distributions which enter the geodesic as well as the geodesic deviation equation. Using a universal regularization procedure we explicitly derive regularization independent distributional limits. In...
متن کامل1 Scalar gravitational waves and Einstein frame
The response of a gravitational wave detector to scalar waves is analysed in the framework of the debate on the choice of conformal frames for scalar-tensor theories. A correction to the geodesic equation arising in the Einstein conformal frame modifies the geodesic deviation equation. This modification is due to the non-metricity of the theory in the Einstein frame, yielding a longitudinal mod...
متن کاملEarly Universe Models from Noncommutative Geometry
We investigate cosmological predictions on the early universe based on the noncommutative geometry models of gravity coupled to matter. Using the renormalization group analysis for the Standard Model with right handed neutrinos and Majorana mass terms, which is the particle physics content of the most recent noncommutative geometry models, we analyze the behavior of the coefficients of the grav...
متن کامل