Related papers: Elastic thick shells in General Relativity
The spectral problem of thin elastic shells in membrane approximation does not satisfy the classical properties of compactness and so there exists an essential spectrum. In the first part, we propose to determinate this spectrum and the…
Two new families of self-consistent axisymmetric truncated equilibrium models for the description of quasi-relaxed rotating stellar systems are presented. The first extends the spherical King models to the case of solid-body rotation. The…
We resolve the entire gravitational field;i.e. the Riemann curvature into its electric and magnetic parts. In general, the vacuum Einstein equation is symmetric in active and passive electric parts. However it turns out that the…
Static spherically symmetric perfect-fluid solutions of Einstein's equations play a central role in relativistic astrophysics and stellar structure theory. While many exact solutions satisfy Einstein's equations mathematically, only a…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how…
We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value…
We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the Einstein-Euler-de Sitter equations. We assume a realistic barotropic equation of state. Equilibria of…
Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic…
We establish the dynamical instability of a static, spherically symmetric, and infinitesimally thin shell in general relativity. The shell is made up of a perfect fluid with a barotropic equation of state, and it produces a Schwarzschild…
We construct a one-parameter family of static and spherically symmetric solutions to the Einstein-Vlasov system bifurcating from the Schwarzschild spacetime. The constructed solutions have the property that the spatial support of the matter…
We consider a prototypical "stretching plus bending" functional of an elastic shell. The shell is modeled as a d-dimensional Riemannian manifold endowed, in addition to the metric, with a reference second fundamental form. The shell is…
The evolution of self-gravitating collision-less matter and scalar waves within the general relativity context is described by Einstein and Vlasov equations. The sources of Einstein equations are generated by a distribution function and a…
A new class of spacetime defect solutions of Einstein Field equations of Edelen's direct Poincar\'{e} Gauge Field theory without biaxial symmetry is presented. The interior solution describes a core of defects where curvature vanishes and…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
We consider a well known model for lipid-bilayer membrane vesicles exhibiting phase separation, incorporating a phase field with finite curvature elasticity. We prove the existence of a plethora of equilibria, corresponding to…