Related papers: A trapped surface in the higher-dimensional self-s…
We revisit the classical results of the formation of trapped surfaces for the Einstein vacuum equation relying on the geodesic foliation, rather than the double null foliation used in all previous results, starting with the seminal work of…
In this article spacelike hypersurfaces immersed in twisted product spacetimes $I\times_f F$ with complete fiber are studied. Several conditions ensuring global hyperbolicity are presented, as well as a relation that needs to hold on each…
The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant…
We study the gravitational collapse of a generalised Vaidya spacetime in the context of the Cosmic Censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed…
It is a standard fact that trapped or marginally trapped surfaces are not visible from conformal infinity, under the usual set of conditions on matter fields and the conformal completion, provided that the cosmological constant is…
We study even parity metric and matter perturbations of all angular modes in self-similar Vaidya space-time. We focus on the case where the background contains a naked singularity. Initial conditions are imposed describing a finite…
We construct new integrable systems to present Weierstrass type representations for spacelike surfaces whose mean curvature vector $\mathbf{H}$ satisfies the null condition $\langle \mathbf{H}, \mathbf{H} \rangle=0$ in the four dimensional…
The occurrence of a spacetime singularity indicates the breakdown of Einstein gravitation theory in these extreme regimes. We consider here the singularity issue and various black hole paradoxes at classical and quantum levels. It is…
Two-dimensional string vacua with Massive Spectrum boson-fermion Degeneracy Symmetry (MSDS) are explicitly constructed in Type II and Heterotic superstring theories. The study of their moduli space indicates the existence of large marginal…
Recently, several new characteristics have been introduced to describe null geodesic structure of strong gravitational field, such as photon regions, transversely trapping surfaces and some generalizations. They give an alternative and…
A maximal surface $\sb$ with isolated singularities in a complete flat Lorentzian 3-manifold $\N$ is said to be entire if it lifts to a (periodic) entire multigraph $\tilde{\sb}$ in $\l^3.$ In addition, $\sb$ is called of finite type if it…
Trapped regions bounded by horizons are the defining features of black holes. However, formation of a singularity-free apparent horizon in finite time of a distant observer is consistent only with special states of geometry and matter in…
In this paper, we study the dynamics of a hollow spherical matter collapsing with very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated…
The theory of embedded random surfaces, equivalent to two--dimensional quantum gravity coupled to matter, is reviewed, further developed and partly generalized to four dimensions. It is shown that the action of the Liouville field theory…
The null surfaces of a spacetime act as one-way membranes and can block information for a corresponding family of observers (time-like curves). Since lack of information can be related to entropy, this suggests the possibility of assigning…
For a two-dimensional surface in the four-dimensional Euclidean space we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and kappa. The condition k = kappa = 0…
A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with…
It has been long known that in spacetimes with a positive cosmological constant $\Lambda >0$ the area of spatially stable marginally trapped surfaces (MTSs) has a finite upper bound given by $4\pi/\Lambda$. In this paper I show that any…
Studying spacetimes with continuous symmetries by dimensional reduction to a lower dimensional spacetime is a well known technique in field theory and gravity. Recently, its use has been advocated in numerical relativity as an efficient…
We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces.…