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Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically…
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 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]…
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…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
We construct time independent configurations describing a small elastic body moving in a circular orbit in the Schwarzschild spacetime. These configurations are relativistic versions of Newtonian solutions constructed previously by us. In…
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…
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…
I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to…
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 perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to…
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…
In this paper we prove the global existence of classical static solutions of Einstein gravitational theory coupled to a real scalar field where the spacetime admits spherically symmetry. The equations of motions can then be reduced into a…
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…
We study the interaction between gravitational waves and elastic bodies within the framework of relativistic elasticity. Starting from the Lagrangian formulation of relativistic elasticity, we derive the linearized equations governing the…
The linear equations of motion of a uniformly rotating, elastic and self-gravitating earth model are analyzed under minimal regularity assumptions. We present existence and uniqueness results for the system, energy estimates, convergence of…
Seven new solutions to the interior static and spherically symmetric Einstein's field equations (EFE) are found and investigated. These new solutions are a generalisation of the quadratic density fall-off profile of the Tolman VII solution.…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…