Related papers: Dynamical compact elastic bodies in general relati…
The classical Euler--Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the motion of the body in space. These generalizations possess…
This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first.…
We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in a class of alternative theories of gravity to general relativity. We use a prescription proposed by Eardley for incorporating…
We develop a theoretical framework to study slowly rotating compact stars in a rather general class of alternative theories of gravity, with the ultimate goal of investigating constraints on alternative theories from electromagnetic and…
In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the…
We consider the most general quadratic in curvature stringy motivated non-local action for the modified Einstein's gravity. We present exact analytic cosmological solutions including the bouncing ones and develop the relevant techniques for…
We prove a global existence theorem (with respect to a geometrically- defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a $T^2$ isometry group with two-dimensional spacelike orbits, acting on $T^3$…
Axisymmetric and stationary solutions are constructed to the Einstein--Vlasov and Vlasov--Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is…
We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve…
In this paper, we found new classes of solutions to the Einstein-Maxwell field equations with matter anisotropic distribution incorporating a particular form of electric field intensity within the framework of general relativity. We use a…
We investigate spherically symmetric equilibrium states of the Vlasov-Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations…
In this paper the dynamic compactification in Lovelock gravity with a cubic term is studied. The ansatz will be of space-time where the three dimensional space and the extra dimensions are constant curvature manifolds with independent scale…
There is described a spacetime formulation of both nonrelativistic and relativistic elasticity. Specific attention is devoted to the causal structure of the theories and the availability of local existence theorems for the initial-value…
We show that the equation of motion for a rigid one-dimensional elastic body (i.e. a rod or string whose speed of sound is equal to the speed of light) in a two-dimensional spacetime is simply the wave equation. We then solve this equation…
A new approach to relativistic elasticity theory is proposed. In this approach the theory becomes a gauge--type theory, with the diffeomorphisms of the material space playing the role of gauge transformations. The dynamics of the elastic…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have shown that, in some specific cases, the vacuum solutions of general relativity are also…
We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…