Related papers: Shadowing high-dimensional Hamiltonian systems: th…
The time irreversibility and fast relaxation of collapsing $N$-body gravitating systems (as opposed to the time reversibility of the equations of motion for individual stars or particles) are traditionally attributed to information loss due…
In this work, starting from a spherically symmetric polytropic black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large…
We study a one dimensional model of gravitational instability in an Einstein-de Sitter universe. Scaling in both space and time results in an autonomous set of coupled Poisson-Vlasov equations for the field and phase space density, and the…
The paper explores the Rutherford scattering shadow in an entire class of comoving frames -- inertial frames moving along the initial projectile direction -- of which the laboratory frame, where the target is initially at rest, is a…
Dark and grey soliton-like states are shown to emerge from numerically constructed superpositions of translationally-invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a…
In a previous paper [arXiv:1308.1852] we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in…
A certain type of matter with anisotropic pressures can add to the Reissner-Nordstr\"om metric a term proportional to a power of the radial coordinate. Using the standard method of separating variables for the Hamilton-Jacobi equation, we…
The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
Contrary to the decades-old understanding, SGn, the Sine-Gordon equation in (1+n) dimensions, has N-soliton solutions for any N >= 1, not only for n = 1, but also for n = 2 and 3. While SG1 solitons are confined to a line, SG2- and…
The investigation of the nonequilibrium quantum dynamics of bosonic many-body systems is very challenging due to the excessively growing Hilbert space and poses a major problem for their theoretical description and simulation. We present a…
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…
Numerical solutions to Newton's equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and…
Quantum effects in general induce scale dependence in the coupling constants. We explore this possibility in gravity, with a scale-dependent Newton coupling. When applied to Kerr black holes with such a running coupling, the consistency of…
We revisit the r\^{o}le of discreteness and chaos in the dynamics of self-gravitating systems by means of $N$-body simulations with active and frozen potentials, starting from spherically symmetric stationary states and considering the…
We investigate late time acceleration of the universe in higher dimensional cosmology. The content in the universe is assumed to exert pressure which is different in the normal and extra dimensions. Cosmologically viable solutions are found…
We examine the shadow of a rotating Kaluza-Klein black hole in Einstein gravity coupled to a Maxwell field and a dilaton. The size and the shape of the shadow depend on the mass, the charge, and the angular momentum of the compact object.…
One method to overcome the notorious problem of time in the quantisation of gravity is the identification of a physically preferred time parameter, a promising candidate being so-called `York time'. The dynamical equations for matter and…