QUANTUM SINGULARITIES IN STATIC AND CONFORMALLY STATIC SPACE-TIMES

Quantization of static space-times

A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-Gordon field. By quantizing canonically the coupling model in the framework of loop quantum gravity, we obtain a quantum theory which actually describes quantized static space-times. The Kinematical Hilbert space is the product of the Hilbert space of gravity with that of im...

Hessian Tensor and Standard Static Space-times

In this brief survey, we will remark the interaction among the Hessian tensor on a semi-Riemannian manifold and some of the several questions in Lorentzian (and also in semi-Riemannian) geometry where this 2−covariant tensor is involved. In particular, we deal with the characterization of Killing vector fields and the study of a set of consequences of energy conditions in the framework of stand...

Quantization of the static space-times

A 4-dimensional Lorentzian static space-time is shown to be equivalent to 3-dimensional Euclidean gravity coupled to an imaginary massless scalar field. By quantizing canonically the coupling model in the framework of loop quantum gravity, we obtain a quantum theory which actually describes quantized static space-times. The Kinematical Hilbert space is the product of the Hilbert space of gravit...

A Remark About Static Space Times

Stationary or static space-times and Young tableaux

1. Introduction The subject of the present paper is the search for examples of Riemann tensors which contain terms with a structure of certain generators of algebraic curvature tensors. Let V be a finite-dimensional K-vector space, where K is the field of real or complex numbers. We denote by T r V the K-vector space of covariant tensors of order r over V .