When simulating the inspiral and coalescence of a binary black-hole system, special care needs to be taken in handling the singularities. Two main techniques are used in numerical-relativity simulations: A first and more traditional one “excises” a spatial neighbourhood of the singularity from the numerical grid on each spacelike hypersurface. A second and more recent one, instead, begins with ...

We study the inner-structure of a charged black-hole which is formed from the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor o...

We study the inner-structure of a charged black-hole which is formed from the gravitational collapse of a self-gravitating charged scalareld. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a nal central singularity. We nd a null, weak, mass-in ation singularity along the Cauchy horizon, which is a precursor of a stro...

We consider the most general vacuum cylindrical spacetimes, which are defined by two global, spacelike, commuting, non-hypersurface-orthogonal Killing vector fields. The cylindrical waves in such spacetimes contain both + and × polarizations, and are thus said to be unpolarized. We show that there are no trapped cylinders in the spacetime, and present a formal derivation of Thorne’s Cenergy, ba...

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface B which bounds a generic spacelike hypersurface Σ of spacetime. The method used to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a suitable covaria...

Eastwood and Ezhov generalized the Cayley surface to the Cayley hypersurface in each dimension, proved some characteristic properties of the Cayley hypersurface and conjectured that a homogeneous hypersurface in affine space satisfying these properties must be the Cayley hypersurface. We will prove this conjecture when the domain bounded by a graph of a function defined on Rn is also homogeneou...

Recent work on an approach to the geometrodynamics of cylindrical gravity waves in the presence of interacting scalar matter fields, based on the Kuchař hypertime formalism, is extended to the analogous spherically symmetric system. This produces a geometrodynamical formalism for spherical black holes and wormholes in which the metric variables are divided into two classes, dynamical and redund...

General Relativity differs from most classical field theories in that there is no welldefined notion of energy density for the gravitation field, as can be seen from Einstein’s principle of equivalence. Thus at best one can only hope to calculate the mass/energy contained within a domain, as opposed to at a point. Such a concept is referred to as quasi-local mass, that is, a functional which as...

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them holds...

In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space L and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational symmetric surfaces are the only compact spacelike surfaces in L of constant mean curvature bounded by two concentric circles in parallel planes. As conclusion, we char...