Related papers: The notes on thin shells
The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2\tau/\hbar) with respect to their continuous masses M and the proper time \tau…
We investigate static, axially symmetric spacetimes without naked singularities that are constructed by patching Weyl class spacetimes with the flat spacetimes. Once the exterior geometry is specified, the junction conditions determine the…
By virtue of harmonic maps on two-dimensional spheres (S$^{2}$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and…
We prove that there can not be a smooth matching of the Generalized Vaidya metric with an exterior Schwarzschild/Vaidya patch across a finite boundary hypersurface unless the mass function is a function of the null coordinate alone. By…
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact…
At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show…
We construct and investigate smooth orientable surfaces in su(N) algebras. The structural equations of surfaces associated with Grassmannian sigma models on Minkowski space are studied using moving frames adapted to the surfaces. The first…
Context: We study the impact of two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from a one-dimensional stellar evolution code are used to produce a model of a large stellar…
The self-interaction for a static point charge in the space-time of a thin-shell wormhole constructed connecting two identical Schwarzschild geometries is calculated in a series expansion. The electrostatic self-force is evaluated…
We investigate proper infall times in the Schwarzschild and Kerr spacetimes from a covariant perspective, focusing on the role of black--hole rotation in the focusing properties of timelike geodesic congruences.To perform a geometrically…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…
Motion of two gravitating spherical stellar shells around a massive central body is considered. Each shell consists of point particles with the same specific angular momenta and energies. In the case when one can neglect the influence of…
The generalized Schwarzschild spacetimes are introduced as warped manifolds where the base is an open subset of $\mathbb{R}^2$ equipped with a Lorentzian metric and the fiber is a Riemannian manifold. This family includes physically…
We consider a spherical thick 3-brane immersed in a five-dimensional bulk spacetime. We demonstrate how the thick brane equation of motion expanded in powers of the thickness of the brane can be obtained from the expected junction…
We analyse the physics of nonlinear gravitational processes inside a spherical charged black hole perturbed by a self-gravitating massless scalar field. For this purpose we created an appropriate numerical code. Throughout the paper, in…
We study spherically symmetric thin-shell wormholes in a string cloud background in (3+1)-dimensional spacetime. The amount of exotic matter required for the construction, the traversability and the stability under radial perturbations, are…
In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…
In the absence of a complete theory of quantum gravity, phenomenological models built upon minimal assumptions have been explored for the analysis of possible quantum effects in gravitational systems. Implications of a superposition of…
In the present study we consider knotted spheres in Euclidean $4$-space $ \mathbb{E}^{4}$. Firstly, we give some basic curvature properties of knotted spheres in $ \mathbb{E}^{4}$. Further, we obtained some results related with the…