Related papers: Relative chaos in gravitating systems with massive…
Self-consistent solutions for triaxial mass models are highly non-unique. In general, some of these solutions might be dynamically unstable, making them inappropriate as descriptions of steady-state galaxies. Here we demonstrate for the…
It is widely believed that structure in the Universe evolves hierarchically, as primordial density fluctuations, amplified by gravity, collapse and merge to form progressively larger systems. The structure and evolution of X-ray clusters,…
We challenge a widely accepted assumption of observational cosmology: that successful reconstruction of observed galaxy density fields from measured galaxy velocity fields (or vice versa), using the methods of gravitational instability…
One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical…
Recent work on the equilibrium and stability of ellipsoidal stellar systems is reviewed. The absence of constant-density cores in early-type galaxies implies that chaos and high-order resonances are generic features of the motion in…
We study the linear stability problem to gravitational and electromagnetic perturbations of the extremal, $ |\mathcal{Q}|=M, $ Reissner-Nordstr\"om spacetime, as a solution to the Einstein-Maxwell equations. Our work uses and extends the…
We prove for generalisations of quasi-homogeneous $n$-body problems with center of mass zero and $n$-body problems in spaces of negative constant Gaussian curvature that if the masses and rotation are fixed, there exists, for every order of…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
The evidence of the phenomenon for which, in galaxies, the gravitating mass is distributed differently than the luminous mass, increases as new data become available. Furthermore, this discrepancy is well structured and it depends on the…
We investigate the possibility of future singularity due to the accelerating expansion of the Universe. It has been found that the gravitational theory comprises Ricci scalar $R$ and Gauss-Bonnet invariant $\mathcal{G}$, known as…
We study the effects of general relativistic gravity on the Hill stability, that is, the stability of a multi-body system against a close approach of one orbit to another, which has been hitherto studied mainly in Newtonian mechanics and…
A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…
The non-linear evolution of one-dimensional perturbations in a three-dimensional expanding Universe is considered. A general Lagrangian scheme is derived, and compared to two previously introduced approximate models. These models are…
Recently a modified version of Rastall theory of gravity has been introduced in which a varying coupling parameter could act as dark energy (DE) and thus, it can be held responsible for the current accelerated expansion of the Universe.…
We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite…
Utilizing a series of N-body simulations, we argue that gravitationally bound stellar clusters of modest population evolve very differently from the picture presented by classical dynamical relaxation theory. The system's most massive stars…
The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…
We study non-axisymmetric oscillations of rapidly and differentially rotating relativistic stars in the Cowling approximation. Our equilibrium models are sequences of relativistic polytropes, where the differential rotation is described by…
Closely-packed multi-planet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A…
Recently, Morrison and Updike showed that many dissipative systems are naturally described as possessing a Riemann curvature-like bracket, which similar to the Poisson bracket, generates the dissipative equations of motion once suitable…