Einstein’s field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a variety of systems self-similar solutions can describe asymptotic or intermediate behaviour of more general solutions. The typical example is the convergence ...

We study 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 of a strong, spacelike singularity along the r = 0 hypersurface. T...

We discuss some geometric problems related to the definitions of quasilocal mass proposed by Brown-York [5] [6] and Liu-Yau [13] [14]. Our discussion consists of three parts. In the first part, we propose a new variational problem on compact manifolds with boundary, which is motivated by the study of Brown-York mass. We prove that critical points of this variation problem are exactly static met...

In the present paper a global conformal invariant Y of a closed initial data set is constructed. A spacelike hypersurface Σ in a Lorentzian spacetime naturally inherits from the spacetime metric a differentiation De, the so-called real Sen connection, which turns out to be determined completely by the initial data hab and χab induced on Σ, and coincides, in the case of vanishing second fundamen...

The topology assumed by most authors for a spacelike hypersurface in a spacetime containing a monopole is generally R3−{0}; save for the surface S2 isolating the monopole, this space is unbounded. For such a topology, a consistency relation of de Rham’s theorems shows that a single isolated monopole cannot exist. Monopoles, with charge ±m, if they exist at all, must occur in pairs having opposi...

We discuss how embeddings in connection with the CampbellMagaard (CM) theorem can have a physical interpretation. We show that any embedding whose local existence is guaranteed by the CM theorem can be viewed as a result of the dynamical evolution of initial data given in a four-dimensional spacelike hypersurface. By using the CM theorem, we establish that for any analytic spacetime, there exis...

The deenition of matter states on spacelike hypersurfaces of a 1+1 dimensional black hole spacetime is considered. The eeect of small quantum uctuations of the mass of the black hole due to the quantum nature of the infalling matter is taken into account. It is then shown that the usual approximation of treating the gravitational eld as a classical background on which matter is quantized, break...

We present numerical simulations of a rotating black hole distorted by a pulse of ingoing gravitational radiation. For strong pulses, we find up to five concentric marginally outer trapped surfaces. These trapped surfaces appear and disappear in pairs, so that the total number of such surfaces at any given time is odd. The world tubes traced out by the marginally outer trapped surfaces are foun...

In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to Einstein-vacuum equations in high dimensions, stable, approximately monotonic curvature singularities can dynamically form along a spacelike hypersurface. this article, we study Cauchy problem and give rigorous proof phenomenon suffici...

Abstract In this article spacelike hypersurfaces immersed in twisted product spacetimes $$I\times _f F$$ I × f F with complete fiber are studied. Several conditions ensuring global hyperbolicity presented, and a r...