Related papers: Static self-gravitating elastic bodies in Einstein…
We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations…
We consider the problem of constructing static, elastic, many-body systems in Einstein gravity. The solutions constructed are deformations of static many-body configurations in Newtonian gravity. No symmetry assumptions are made.
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of…
The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6]…
There is proved an existence theorem, in the Newtonian theory, for static, self-gravitating bodies composed of elastic material. The theorem covers the case where these bodies are small, but allows them to have arbitrary shape.
We consider elastic bodies in rigid rotation, both nonrelativistically and in special relativity. Assuming a body to be in its natural state in the absence of rotation, we prove the existence of solutions to the elastic field equations for…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein…
The existence and stability of the Einstein static solution have been built in the Einstein-Cartan gravity. We show that this solution in the presence of perfect fluid with spin density satisfying the Weyssenhoff restriction is cyclically…
Well-posedness for the initial value problem for a self-gravitating elastic body with free boundary in Newtonian gravity is proved. In the material frame, the Euler-Lagrange equation becomes, assuming suitable constitutive properties for…
We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in…
We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy…