Related papers: A concise introduction to trapped surface formatio…
Recently, the gravitational collapse of an infinite cylindrical thin shell of matter in an otherwise empty spacetime with two hypersurface orthogonal Killing vectors was studied by Gon\c{c}alves [Phys. Rev. {\bf D65}, 084045 (2002).]. By…
This paper investigates the global properties of a class of spherically symmetric spacetimes. The class contains the maximal development of asymptotically flat spherically symmetric initial data for a wide variety of coupled Einstein-matter…
For gravitational collapse, we observe a correspondence between region close to past null infinity and region close to central singularity. In line with this philosophy, we construct a new ansatz, with which we first present a 40-page…
We study trapped surfaces from the point of view of local isometric embedding into three-dimensional Riemannian manifolds. When a two-surface is embedded into three-dimensional Euclidean space, the problem of finding all surfaces applicable…
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…
We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her…
Objectives: A systematic study on the general relativistic Poynting-Robertson effect has been developed so far by introducing different complementary approaches, which can be mainly divided in two kinds: (1) improving the theoretical…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
This article discusses methods of geometric analysis in general relativity, with special focus on the role of "critical surfaces" such as minimal surfaces, marginal surface, maximal surfaces and null surfaces.
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
Optical trapping is a widely used technique, with many important applications in biology and metrology. Complete modelling of trapping requires calculation of optical forces, primarily a scattering problem, and non-optical forces. The…
We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible…
We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped…
Klainerman, Luk and Rodnianski derived an anisotropic criterion for formation of trapped surfaces in vacuum, extending the original trapped surface formation theorem of Christodoulou. The effort to understand their result led us to study…
We predict that spatial self-trapping of light can occur in soft matter encompassing a wide class of new materials such as colloids, foams, gels, fractal aggregates etc. We develop a general nonlocal theory that allows to relate the…
We demonstrate that the Penrose inequality is valid for spherically symmetric geometries even when the horizon is immersed in matter. The matter field need not be at rest. The only restriction is that the source satisfies the weak energy…
This preprint concerns a mathematically rigorous treatment of an interesting physical phenomenon in relativity theory. We would like to draw the reader's attention particularly to the abstract mathematical formalism of relativity (which was…
An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on…
We provide an informal discussion of pattern formation in a finite universe. The global size and shape of the universe is revealed in the pattern of hot and cold spots in the cosmic microwave background. Topological pattern formation can be…