Chaplygin Gravitodynamics

We consider a new approach for gravity theory coupled to Chaplygin matter in which the {\it{relativistic}} formulation of the latter is of crucial importance. We obtain a novel form of matter with dust like density $(\sim (volume)^{-1})$ and negative pressure. We explicitly show that our results are compatible with a relativistic generalization of the energy conservation principle, derived here.Comment: Title changed, Revised version,N o change in conclusions, Journal ref.: MPL A21 (2006)1511-151

On a family of integrable systems on S2S^2 with a cubic integral of motion

We discuss a family of integrable systems on the sphere $S^2$ with an additional integral of third order in momenta. This family contains the Coryachev-Chaplygin top, the Goryachev system, the system recently discovered by Dullin and Matveev and two new integrable systems. On the non-physical sphere with zero radius all these systems are isomorphic to each other.Comment: LaTeX, 8 page

Self-gravitating clouds of generalized Chaplygin and modified anti-Chaplygin Gases

The Chaplygin gas has been proposed as a possible dark energy, dark matter candidate. As a working fluid in a Friedmann-Robertson-Walker universe, it exhibits early behavior reminiscent of dark matter, but at later times is more akin to a cosmological constant. In any such universe, however, one can expect local perturbations to form. Here we obtain the general equations for a self-gravitating relativistic Chaplygin gas. We solve these equations and obtain the mass-radius relationship for such structures, showing that only in the phantom regime is the mass-radius relationship large enough to be a serious candidate for highly compact massive objects at the galaxy core. In addition, we study the cosmology of a modified anti-Chaplygin gas. A self-gravitating cloud of this matter is an exact solution to Einstein's equations.Comment: 16 page

Chaplygin gas with non-adiabatic pressure perturbations

Perturbations in a Chaplygin gas, characterized by an equation of state $p = -A/\rho$, may acquire non-adiabatic contributions if spatial variations of the parameter $A$ are admitted. This feature is shown to be related to a specific internal structure of the Chaplygin gas. We investigate how perturbations of this type modify the adiabatic sound speed and influence the time dependence of the gravitational potential which gives rise to the Integrated Sachs-Wolfe effect in the anisotropy spectrum of the cosmic microwave background.Comment: 16 pages, comments and references added, accepted for publication in Class.Quantum Gra

FRW Quantum Cosmology with a Generalized Chaplygin Gas

Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. We consider the hypothesis that the transition to the accelerated period involves a quantum mechanical process. Three physically admissible cases are possible. In particular, we identify a minisuperspace configuration with two Lorentzian sectors, separated by a classically forbidden region. The Hartle-Hawking and Vilenkin wave functions are computed, together with the transition amplitudes towards the accelerating epoch. Furthermore, it is found that for specific initial conditions, the parameters characterizing the generalized Chaplygin gas become related through an expression involving an integer $n$. We also introduce a phenomenological association between some brane-world scenarios and a FRW minisuperspace cosmology with a generalized Chaplygin gas. The aim is to promote a discussion and subsequent research on the quantum creation of brane cosmologies from such a perspective. Results suggest that the brane tension would become related with generalized Chaplygin gas parameters through another expression involving an integer.Comment: 13 pages, 3 figures, RevTeX

On integrable system on S2S^2 with the second integral quartic in the momenta

We consider integrable system on the sphere $S^2$ with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system.Comment: LaTeX, 6 page

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material from arXiv:1109.321

Role of Modified Chaplygin Gas as a Dark Energy Model in Collapsing Spherically Symmetric Cloud

In this work, gravitational collapse of a spherical cloud, consists of both dark matter and dark energy in the form of modified Chaplygin gas is studied. It is found that dark energy alone in the form of modified Chaplygin gas forms black hole. Also when both components of the fluid are present then the collapse favors the formation of black hole in cases the dark energy dominates over dark matter. The conclusion is totally opposite to the usually known results.Comment: 7 Latex Pages, RexTex style, No figure

Collisionless kinetic theory of rolling molecules

We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of statistical physics. In particular, we show that even though the energy of the system is conserved, and the system is closed in the thermodynamic sense, some fundamental features of statistical physics such as invariant measure do not hold for such nonholonomic systems. Nevertheless, we are able to construct a consistent kinetic theory using Hamilton's variational principle in Lagrangian variables, by regarding the kinetic solution as being concentrated on the constraint distribution. A cold fluid closure for the kinetic system is also presented, along with a particular class of exact solutions of the kinetic equations.Comment: Revised version; 31 pages, 1 figur

Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure