Related papers: Surface Layers in General Relativity and Their Rel…
In this lecture we deal with the construction of surface densities for the angular momentum of the sources of asymptotically flat vacuum stationary axisymmetric spacetimes. These sources arise from the discontinuities of the twist…
The approach of global isomorphism between the fluid and the Ising model is applied to obtain an expression for the surface tension of the Lennard-Jones fluid on the basis of the information about the Ising model. This is done in a broad…
We show that closed hypersurfaces in Euclidean space with nonnegative scalar curvature are weakly mean convex. In contrast, the statement is no longer true if the scalar curvature is replaced by the k-th mean curvature, for k greater than…
For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure,…
Spacelike surfaces in Generalized Robertson-Walker spacetimes whose mean curvature function satisfies a natural nonlinear inequality are analyzed. Several uniqueness and nonexistence results for such compact spacelike surfaces are proved.…
For asymptotically flat spacetimes, using the inverse mean curvature flow, we show that any compact $2$-surface, $S_0$, whose mean curvature and its derivative for outward direction are positive in spacelike hypersurface with non-negative…
As is well known, the 0 - 0 component of the Schwarzschild space can be obtained by the requirement that the geodesic of slowly moving particles match the Newtonian equation. Given this result, we show here that the remaining components can…
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…
Combining the intrinsic and extrinsic geometry, we generalize Einstein manifolds to Integral-Einstein (IE) submanifolds. A Takahashi-type theorem is established to characterize minimal hypersurfaces with constant scalar curvature (CSC) in…
We numerically check that the surface tension of membranes is independent of the shape of surface boundary. The surface tension is calculated by means of the Monte Carlo simulation technique on two types of cylinders made of rubans of size…
We consider the dynamics of a layer of an incompressible electrically conducting fluid interacting with the magnetic field in a two-dimensional horizontally periodic setting. The upper boundary is in contact with the atmosphere, and the…
Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a…
The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the…
We study the magnitude of semiclassical gravity effects near the formation of a black-hole horizon in spherically-symmetric spacetimes. As a probe for these effects we use a quantised massless scalar field. Specifically, we calculate two…
The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint $q \to 0$ limit, with $q$ the degree of freedom normal to the surface. In this…
We consider an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of ideal compressible magnetohydrodynamics (MHD), while the electric and magnetic…
The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of…
In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume comparison theorem involving scalar curvature for…
A Monte Carlo (MC) study is performed to evaluate the surface tension $\gamma $ of spherical membranes that may be regarded as the models of the lipid layers. We use the canonical surface model defined on the self-avoiding triangulated…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…