The instability analysis of self-gravitation systems under the perturbation with orbital angular momentum

Based on plasma kinetic theory, the instabilities of self-gravitation systems under perturbation with orbital angular momentum(OAM) are investigated, and the concept of twisted Jeans mode is introduced to describe the new phenomenon. The result shows that the growth rate of the Jeans instability is enhanced with the OAM parameter increased, while the critical wave number is consistent with the classical Jeans critical value. It is expected that the present results would give more insight into the evolution and dynamics of a self-gravitational system.

Single Mode Periodic Wave Trains in Self-Gravitating Dusty Plasma

In this paper, we consider the dynamics of modulated waves in an unmagnetized, non-isothermal self-gravitating dusty plasma model. The varying charge on the moving dust, as it moves in and out of regions of differing electron and ion densities (due to changes in the electrostatic potential), will be out of phase with the equilibrium charge. The effect of the dust is to increase the phase velocity of the ion-acoustic (IA) waves i.e. decrease the Landau damping. In the low-amplitude limit and weak damping, we apply the reductive perturbation method on the model that resulted to the complex cubic Ginzburg-Landau (CCGL) equation. From these results, it is observed that, the plasma parameters strongly influence the properties of the solitary wave solution namely, the amplitude and the width. The effects of non-isothermal electrons, gravity, dust charge fluctuations and drifting motion on the ion-acoustic solitary waves are discussed with application in astrophysical contexts. It is also observed that the number of charges residing on the dust grains increases the modulational stability of the plane waves in the plasma, thus, enhancing the generation of modulated waves.

Instabilities in a Self-Gravitating Magnetized Gas Disk

A linear stability analysis has been performed onto a self-gravitating magnetized gas disk boundxed by external pressure. The resulting dispersion relation is fully explained by three kinds of instability: a Parker-type instability driven by self-gravity, usual Jeans gravitational instability and convection. In the direction parallel to the magnetic fields, the magnetic tension completely suppresses the convection. If the adiabatic index γ is less than a certain critical value, the perturbations trigger the Parker as well as the Jeans instability in the disk. Consequently, the growth rate curve has two maxima: one at small wavenumber due to a combination of the Parker and Jeans instabilities, and the other at somewhat larger wavenumber mostly due to the Parker instability. In the horizontal direction perpendicular to the fields, the convection makes the growth rate increase monotonically upto a limiting value as the perturbation wavenumber gets large. However, at small wavenumbers, the Jeans instability becomes effective and develops a peak in the growth rate curve. Depending on the system parameters, the maximum growth rate of the convection may or may not be higher than the peak due to the Jeans-Parker instability. Therefore, a cooperative action of the Jeans and Parker instabilities can have chances to over-ride the convection and may develop large scale structures of cylindrical shape in non-linear stage. In thick disks the cylinder is expected to align its axis perpendicular to the field, while in thin ones parallel to it.

Nonlinear acoustic waves in a collisional self-gravitating dusty plasma

Using the reductive perturbation method, we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma. The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation, and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.

Nucleus-acoustic solitary waves in self-gravitating degenerate quantum plasmas

Nucleus-acoustic（NA） solitary waves（SWs） propagating in a self-gravitating degenerate quantum plasma（SDQP）system（containing non-relativistically degenerate heavy and light nuclei,and non-/ultra-relativistically degenerate electrons） have been theoretically investigated.The modified Korteweg–de Vries（m K-d V） equation has been derived for both planar and non-planar geometry by employing the reductive perturbation technique.It is shown that the NA SWs exist with positive（negative） electrostatic（self-gravitational） potential.It is also observed that the effects of non-/ultra-relativistically degenerate electron pressure,dynamics of non-relativistically light nuclei,spherical geometry,etc.significantly modify the basic features（e.g.,amplitude,width,speed,etc.） of the NA SWs.The applications of our results,which are relevant to astrophysical compact objects,like white dwarfs and neutron stars,are briefly discussed.

Statistical Induced Dynamic of Self-Gravitating System

The self-gravitating systems a priory are non-equilibrium. The new approach, based on non-equilibrium statistical operator, which allows taking into account inhomogeneous distribution of particles and temperature, has been proposed. Such method employs a saddle point procedure to find dominant contributions to the partition function and permits to obtain all thermodynamic parameters of the system. Statistical induced dynamic and behavioral peculiarities of self-gravitating systems for different conditions have been predicted.

Instability of Thermally Conducting Self-Gravitating Systems

The gravitational instability of a thermally conducting self-gravitating system permeated by a uniform and oblique magnetic field has been analyzed in the framework of Tsallis’ nonextensive theory for possible mod-ifications in the Jeans’ instability criterion. It is concluded that the instability criterion is indeed modified into one that depends explicitly on the nonextensive parameter. The influence of thermal conductivity on the system stability is also examined.

Tunnelling effect of the non-stationary Kerr black hole

Extending Parikh and Wilczek＇s work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilto-Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.

Kinetic theory of Jeans'gravitational instability in millicharged dark matter system

The possibility of baryons cooled by a millicharged dark matter(mDM)via mDM–baryons scattering has recently been proposed to explain the observation discrepancy from the experiment to detect the global epoch of reionization signature(EDGES).In this sense,we analyze the Jeans instability of self-gravitational systems in the background of mDM under kinetic regime that the collisionless Boltzmann equation and Poisson equation have been combined to obtain the modified dispersion relation.It is shown that the effect of mDM is significant on the dynamics of gravitational collapse,i.e.,the presence of mDM makes the self-gravitational systems more difficult to collapse relatively.

Blow-up of Viscous Compressible Reactive Self-gravitating Gas

In this paper, we prove some results concerning blow-up of viscous compressible reactive （selfgravitating） flows when the initial density is compactly supported and the other initial value satisfy proper conditions. It extends the work of Xin and Cho to the case of viscous compressible reactive self-gravitating flows equations. We control the lower bound of second moment by total energy and obtain the precise relationship between the size of the support of initial density and the existence time.

Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory

Thermodynamics plays an important role in gravitational theories.It is a principle that is independent of gravitational dynamics,and there is still no rigorous proof to show that it is consistent with the dynamical principle.We consider a self-gravitating perfect fluid system with the general diffeomorphism-covariant purely gravitational theory.Based on the Noether charge method proposed by Iyer and Wald,considering static off/on-shell variational configurations,which satisfy the gravitational constraint equation,we rigorously prove that the extrema of the total entropy of a perfect fluid inside a compact region for a fixed total particle number demands that the static configuration is an on-shell solution after we introduce some appropriate boundary conditions,i.e.,it also satisfies the spatial gravitational equations.This means that the entropy principle of the fluid stores the same information as the gravitational equation in a static configuration.Our proof is universal and holds for any diffeomorphism-covariant purely gravitational theories,such as Einstein gravity,f(R)gravity,Lovelock gravity,f(Gauss-Bonnet)gravity and Einstein-Weyl gravity.Our result indicates the consistency between ordinary thermodynamics and gravitational dynamics.