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Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
When a thin sheet is crushed into a small three-dimensional volume, it invariably forms a structure with a low volume fraction but high resistance to further compression. Being a far-from-equilibrium process, forced crumpling is not…
We make observations about constant mean curvature surfaces in Euclidean 3-space and their dual surfaces, and the resulting pairs of surfaces in hyperbolic 3-space under the Lawson correspondence.
We study the Einstein gravity equations projected on a timelike surface, which represents the time evolution of what we call a gravitational screen. We show that such a screen behaves like a viscous bubble with a surface tension and an…
The paper considers a set of equations describing the static isotropic gravity field of a macroscopic body within the framework of the theory of gravity with a constraint. A general approximate solution of these equations is obtained. The…
We establish a general `gluing theorem', which states roughly that if two nondegenerate constant mean curvature surfaces are juxtaposed, so that their tangent planes are parallel and very close to one another, but oppositely oriented, then…
Recent calculations have shown that the linear proportionality between black hole entropy and area can be explained by performing a density matrix calculation for a massless free field theory. By applying the same formalism to an empirical…
Here we consider the generalized Oppenheimer-Snyder collapse of a star into a four-dimensional Einstein-Gauss-Bonnet black hole as well as a class of regular black holes labeled by the polytropic index of the stellar matter. We then analyze…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
Surface tension (S) is due to the inward force experienced by particles at the surface and usually gravitation does not play an important role in this force. But in compact stars the gravitational force on the particles is very large and S…
We study spherically symmetric timelike thin-shells in $3+1-$dimensional bulk spacetime with a variable equation of state for the fluid presented on the shell. In such a fluid the angular pressure $p$ is a function of both surface energy…
Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which…
Coefficients of surface tension for even-even nuclei were estimated using its dependence of nuclear rigidity. The values of nuclear rigidity were obtained owing to its connection to mean squared deformations. The correlation of estimated…
We develop a global theory for complete hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. This theory extends the usual one of constant mean curvature hypersurfaces in…
Spacelike surfaces in the Lorentz-Minkowski space L^3 can be endowed with two different Riemannian metrics, the metric inherited from L^3 and the one induced by the Euclidean metric of R^3. It is well known that the only surfaces with zero…
Hypersurfaces of arbitrary causal character embedded in a spacetime are studied with the aim of extracting necessary and sufficient free data on the submanifold suitable for reconstructing the spacetime metric and its first derivative along…
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.…
In the present paper, we propose a new discrete surface theory on 3-valent embedded graphs in the 3-dimensional Euclidean space which are not necessarily discretization or approximation of smooth surfaces. The Gauss curvature and the mean…