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...

In his paper Mc], whose object was to show that the spectrum of the Laplacian of a Riemannian surface S determines the surface up to nitely many possibilities , Henry McKean proved the following result, which he called the \Riemann hypothesis for Riemann surfaces": Theorem (McKean Mc]). If S is a hyperbolic Riemann surface, then the rst eigenvalue 1 (S) of the Laplacian on S satisses 1 (S) 14: ...

We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic expansion in powers of a radial coordinate. The coefficients of the expansion are analytic functions of the angles. This result allow us to fill a gap in the p...

In this paper, we characterize the complete space-like submanifolds with parallel mean curvature vector satisfying H2 = 4(n−1)c n2 in the de Sitter space completely.

It is well known that the semi-Riemannian (pseudo-Riemannian) manifolds (M,g) of Lorentzian signature play a special role in geometry and physics, and that they are models of space time of general relativity. Let Mn+1 p (c) be an (n+1)-dimensional complete connected semi-Riemannian manifold with constant sectional curvature c and index p (see [13, page 227]). It is called an indefinite space fo...

R. Baldini, E Pasqualucci INFN Laboratori Nazionali di Frascati, Italy S. Dubnička Ist. of Physics, Slovak Acad. of Sciences, Bratislava P. Gauzzi Dipartimento di Fisica dell’Università and INFN, Roma S. Pacetti Dipartimento di Fisica dell’Università and INFN, Perugia Y. Srivastava Dipartimento di Fisica dell’Università and INFN, Perugia, Italy and Physics Departement, Northeastern University, ...

Friedrich’s proofs for the global existence results of de Sitter-like space-times and of semiglobal existence of Minkowski-like space-times [Comm. Math. Phys. 107, 587 (1986)] are re-examined and discussed, making use of the extended conformal field equations and a gauge based on conformal geodesics. In this gauge the location of the conformal boundary of the space-times is known a priori once ...