Related papers: Static self-gravitating many-body systems in Einst…
We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Riemann ellipsoids having at least two equal axes.
Einstein equations with $T_{\mu\nu} = k_\mu k_\nu + \ell_\mu \ell_\nu$ where $k, \ell$ are null are considered with spherical symmetry and staticity. The solution has naked singularity and is not asymptotically flat. However, it may be…
This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a field…
The role of gravity is crucial in astrophysics. It determines the evolution of any system, over an enormous range of time and space scales. Astronomical stellar systems as composed by N interacting bodies represent examples of…
This paper investigates the existence and stability of Einstein universe in the context of $f(R,T,Q)$ gravity, where $Q=R_{\mu\nu}T^{\mu\nu}$. Considering linear homogeneous perturbations around scale factor and energy density, we formulate…
Several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. In this paper we address the subtle question of ambiguities in the nature of two dimensional gravity in an…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
Complications arising from the non-compact nature of the phase space of N-body systems prevent any asymptotic characterization of chaotic behaviour (since no equilibrium final states can exist). This leads us to revisit some of the old…
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…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
Here we propose a new method to study gravitational stability of the solutions to the Einstein equations. This method uses the canonical superenergy density and it is different from approaches already used (Lyapunov's stability, dynamical…
We consider some elementary features of Newtonian gravity, or electrostatics, as defined on an N-sphere. In particular, we present and discuss "the shell theorem" for this system.
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…
In this paper we study the linear stability of relative equilibria in the Newtonian $n$-body problem from the viewpoint of electromagnetic systems. We first examine the effect of the ambient dimension on stability, starting from the…
In self-gravitating $N$-body systems, small perturbations introduced at the start, or infinitesimal errors that are produced by the numerical integrator or are due to limited precision in the computer, grow exponentially with time. For…
The study of the dynamics of a two-body system in modified gravity constitutes a more complex problem than in Newtonian gravity. Numerical methods are typically needed to solve the equations of geodesics. Despite the complexity of the…
We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a…
We formulate and approximately solve a specific many-body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving…
We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we…