Null surfaces in 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...

Asymptotically Stationary and Static Space-times and Shear Free Null Geodesic Congruences

In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus ’i’ magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex dipole moment vanishes. Analogously in asymptotically flat space-times it has been shown that one can determine the complex center of mass by transforming the ...

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