Zum Kollapsproblem in Gravitationstheorien

In competing gravitational theories the gravitational collapse is discussed by means of a simple model of a star proposed by Einstein in 1939 (point-particle cluster). In the framework of this model the existence of circular motions of test particles for all values of radii is a criterion for the avoidance of gravitational collapse. Classical theories of gravitation in which the principle of causality is postulated additionally as much as relativistic theories of gravitation are compared with respect to the collapse behaviour. It is shown that circular motions are possible for all values of radii within the inertial-free mechanics proposed by Treder.     

Some secondary indications of gravitational collapse

A stellar core becomes somewhat less massive due to neutrinos radiated away during its collapse in a neutron star or a black hole. The paper deals with the hydrodynamic motion of stellar envelope induced by such a mass loss. Depending on the structure of the outer stellar layers, the motion results either in ejection of an envelope with mass and energy proper for Nova outbursts; or nearly instantaneous excitation of strong pulsations of the star; or lastly in a slow slipping away of the whole stellar envelope. These phenomena are of importance when more powerful events, like supernova outbursts presumably associated with gravitational collapse, are absent. Such secondary indications of gravitational collapse are of special interest, since they may be a single observable manifestation (besides neutrinos and gravitational waves) of massive black hole formation.     

Relativistic gravitational collapse of a cool white dwarf with allowance for the neutronization kinetics

We consider and numerically solve the problem of the relativistic gravitational collapse of a spherically symmetric cool nonrotating white dwarf with allowance for the neutronization kinetics. We propose a model equation of state and analyze the neutronization kinetics under simplifying assumptions. A comprehensive mathematical model is constructed for the phenomenon. The system of equations is integrated numerically. The gravitational collapse of a white dwarf that lost its stability is shown to lead to the envelope ejection and to the final state of a hot static neutron star. For comparison, we solve the problem with an equilibrium equation of state. We show that in this case, the entire mass ultimately goes under the gravitational radius to form a black hole.     

Three-dimensional calculations of the formation of the presolar nebula from a slowly rotating cloud

The presolar nebula may have formed from the collapse of a very slowly rotating interstellar cloud. The first three-dimensional, hydrodynamical calculations of the collapse of such clouds are presented. The models include radiative transfer in the Eddington approximation, as well as detailed equations of state appropriate for the nonisothermal regime of protostellar evolution. Very slowly rotating clouds, i.e., those with initial ratios of rotational energy to gravitational energy of 10^?3 or less, avoid fragmentation and instead collapse to form single central objects, containing quasistatic cores with densities of about 10^?10 g cm^?3. These cores are, however, surrounded by significantly nonaxisymmetric regions, such that the presolar nebula would have been bar-like over the scale of the present solar system. This nonaxisymmetry, coupled with differential rotation, results in gravitational torques that produce rapid outward transfer of angular momentum. The center of the presolar nebula should then be able to contract and collapse to pre-main-sequence densities without suffering fission or fragmentation.     

Dynamics of non-adiabatic charged cylindrical gravitational collapse

This paper is devoted to study the dynamics of gravitational collapse in the Misner and Sharp formalism. We take non-viscous heat conducting charged anisotropic fluid as a collapsing matter with cylindrical symmetry. The dynamical equations are derived and coupled with the transport equation for heat flux obtained from the Müller-Israel-Stewart causal thermodynamic theory. We discuss the role of anisotropy, electric charge and radial heat flux over the dynamics of the collapse with the help of coupled equation.     

Alfvén-Jeans and Magnetosonic Modes in Multispecies Self-Gravitating Dusty Plasmas

Perpendicularly propagating electromagnetic waves in magnetized, multispecies, self-gravitating dusty plasmas are investigated in terms of their wave dispersion properties as well as with respect to their susceptibility to gravitational collapse. In particular, waves on the ordinary as well as extraordinary mode branches are considered. Within the one-dimensional propagation model employed, all modes except the ordinary mode produce density perturbations that can be unstable to gravitational collapse. The wavelengths that are unstable are comparable to the well-known Jeans length for a neutral gas/dust, but there are interesting modifications due to the presence of a magnetic field and charged particles. Furthermore, the effects of the gravitational coupling of a multicomponent plasma to a neutral dust are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Amplification of primordial magnetic fields by anisotropic gravitational collapse

If a magnetic field is frozen into a plasma that undergoes spherical compression, then the magnetic field B varies with the plasma density ρ according to   B ∝ρ^2/3  . In the gravitational collapse of cosmological density perturbations, however, quasi-spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using a relation of the form   B ∝ρ^α  , we show that the median value of α can be much larger than the value  α= 2/3  resulting from spherical collapse, even if there is no initial correlation between magnetic field and principal collapse directions. These analytic arguments go some way towards understanding the results of numerical simulations.     

The collapse of iron-oxygen stars: Physical and mathematical formulation of the problem and computational method

A statement of the problem of gravitational collapse and a computational method are described. The main feature of the collapse — its extremely high heterogeneity — is taken into account. The structure of a collapsing star is characterized by a dense and hot nucleon core which is opaque with respect to neutrino radiation and is embedded in to and extended envelope, almost transparent to neutrinos. The envelope is gradually being accreted onto the core. The enormous amount of energy, radiated in the form of neutrinos and antineutrinos, make us pay particular attention to relatively small absorption of neutrino radiation by extended envelope (so-called energy of deposition). The inclusion of the energy deposition in the calculations is of importance for the problem of transformation of an implosion into an explosion. The deposition is taken into consideration in the approximation of diluted neutrino radiation which escapes from neutrino photosphere and is partially absorbed in the envelope. Both the generation of energy due to deposition and the change of neutronto-proton ratio are taken into account. The increase of the mass of the core, which is opaque with respect to neutrino radiation, is fully taken into account in the calculations of the gravitational collapse.     

Gravitational collapse of a massive sphere of constant energy density

Gravitational collapse of a massive sphere of constant density has been studied from the point of view of a Keplerian observer. The asymptotic nature of collapse is attributed to the development of negative gravitational pressure acting radially outwards within the structure. The region of negative pressure asymptotically covers the entire interior asu=mass/radius tends to half.     

Acceleration of charged particles in the magnetosphere of a collapsing star and their nonthermal electromagnetic radiation

We investigate a transformation of a magnetic field and plasma in nonhomogeneous magnetospheres of collapsing stars with a dipole initial magnetic field and certain initial energy distributions of particles in the magnetosphere as the power low, relativistic Maxwell and Boltzmann. The betatron mechanism of the charged particles acceleration in a collapsing star’s magnetosphere is considered. When a magnetized star is compressed in the stage of the gravitational collapse, the magnetic field increases strongly. This variable magnetic field generates a vortical electric field. Our calculations show that this electric field will accelerate charged particles up to relativistic velocities. Thus, collapsing stars may be sources of high energy cosmic rays in our galaxy as in others. The acceleration of particles during the collapse happens mostly in polar regions of the magnetosphere that leads to polar relativistic streams (jets) formation. When moving in a magnetic field, these particles will generate nonthermal electromagnetic radiation in a broad electromagnetic wavelength band from radioto gamma rays. Thus, in the stage of the gravitational collapse, relativistic jets are formed in stellar magnetospheres. These jets are powerful sources of the nonthermal electromagnetic radiation.     

Quasi-spherical collapse with cosmological constant

The junction conditions between static and non-static space–times are studied for analysing gravitational collapse in the presence of a cosmological constant. We have discussed about the apparent horizon and their physical significance. We also show the effect of cosmological constant in the collapse and it has been shown that cosmological constant slows down the collapse of matter.     

Effects of electromagnetic field on the collapse and expansion of anisotropic gravitating source

This paper is devoted to study the effects of electromagnetic on the collapse and expansion of anisotropic gravitating source. For this purpose, we have evaluated the generating solutions of Einstein–Maxwell field equations with spherically symmetric anisotropic gravitating source. We found that a single function generates the various anisotropic solutions. In this case every generating function involves an arbitrary function of time which can be chosen to fit several astrophysical time profiles. Two physical phenomenon occur, one is gravitational collapse and other is the cosmological expanding solution. In both cases electromagnetic field effects the anisotropy of the model. For collapse the anisotropy is increased while for expansion it deceases from maximum value to finite positive value. In case of collapse there exits two horizons like in case of Reissner–Nordström metric.     

Collapsing index: a new method to identify star-forming cores based on ALMA images

Stars form through the gravitational collapse of molecular cloud cores.Before collapsing,the cores are supported by thermal pressure and turbulent motions.A question of critical importance for the understanding of star formation is how to observationally discern whether a core has already initiated gravitational collapse or is still in hydrostatic balance.The canonical method to identify gravitational collapse is based on the observed radial density profile,which would change from Bonnor-Ebert type toward power laws as the core collapses.In practice,due to the projection effect,the resolution limit and other caveats,it has been difficult to directly reveal the dynamical status of cores,particularly in massive star forming regions.We here propose a novel,straightforward diagnostic,namely,the collapsing index(CI),which can be modeled and calculated based on the radial profile of the line width of dense gas.A meaningful measurement of CI requires spatially and spectrally resolved images of optically thin and chemically stable dense gas tracers.ALMA observations are making such data sets increasingly available for massive star forming regions.Applying our method to one of the deepest dense-gas spectral images ever taken toward such a region,namely,the Orion molecular cloud,we detect the dynamical status of selected cores.We observationally distinguished a collapsing core in a massive star forming region from a hydrostatical one.Our approach would help significantly improve our understanding of the interaction between gravity and turbulence within molecular cloud cores in the process of star formation.     

Plane symmetric gravitational collapse and linear equation of state

This paper examines the gravitational collapse in plane symmetry with a perfect fluid using a linear equation of state p=kρ. We find a class of collapse models satisfying the Einstein field equations and also the regularity as well as energy conditions. For a given initial data, the outcome of the collapse turns out to be a black membrane or a naked singularity depending upon the equation of state parameter. We conclude that this parameter plays a crucial role in determining the final fate of the collapse.     

Gravitational radiation from the collapse and explosion of rapidly rotating,homogeneous, gaseous ellipsoids imbedded in halos

The nonlinear motion (collapse/explosion) of a homogeneous, rapidly rotating, gaseous ellipsoid has been studied with the effects of an external gravitational field incorporated. The non-axisymmetric motion has been followed using an efficient numerical code based on certain properties of the potential functions. The gravitational radiation associated with the phenomenon was calculated, and the wave forms studied to extract information on the dynamics of the source. Possible implications of our results for various astrophysical processes are discussed.     

引力坍缩能形成环星系吗?

大部分环星系是由星系相互作用、引力响应的演化形成．但是，这并不是形成环星系的唯一方式．孤立星系的引力坍缩也可能形成环星系．本文进行引力坍缩的数值模拟试验，计算结果也显示出较好的环形结构．     

A generalization of the concept of adiabatic index for non-adiabatic systems

The concept of adiabatic index, measuring the stiffness of the equation of state for adiabatic systems, and which plays a fundamental role in the study of gravitational collapse, is extended to systems emitting and/or absorbing energy. In the light of the new definition, the collapse of two models of radiating, general relativistic spheres is analyzed in detail, at different regimes of radiation transport. The conspicuous role played by the new variable is clearly exhibited.     

Thermodynamics of a model of nonadiabatic spherical gravitational collapse

In this work, a thermodynamic treatment of a Friedmann-like model of nonadiabatic spherical gravitational collapse is presented. The calculations have been performed according to Eckart's theory of dissipative relativistic fluids, while the diffusion approximation has been adopted for the radiation transport. The conclusions deduced are in agreement with the predictions of the theory of late stellar evolution.     

Formation of stars and planets: the role of magnetic fields

Star formation is thought to be triggered by gravitational collapse of the dense cores of molecular clouds. Angular momentum conservation during the collapse results in the progressive increase of the centrifugal force, which eventually halts the inflow of material and leads to the development of a central mass surrounded by a disc. In the presence of an angular momentum transport mechanism, mass accretion onto the central object proceeds through this disc, and it is believed that this is how stars typically gain most of their mass. However, the mechanisms responsible for this transport of angular momentum are not well understood. Although the gravitational field of a companion star or even gravitational instabilities (particularly in massive discs) may play a role, the most general mechanisms are turbulence viscosity driven by the magnetorotational instability (MRI), and outflows accelerated centrifugally from the surfaces of the disc. Both processes are powered by the action of magnetic fields and are, in turn, likely to strongly affect the structure, dynamics, evolutionary path and planet-forming capabilities of their host discs. The weak ionisation of protostellar discs, however, may prevent the magnetic field from effectively coupling to the gas and shear and driving these processes. Here I examine the viability and properties of these magnetically-driven processes in protostellar discs. The results indicate that, despite the weak ionisation, the magnetic field is able to couple to the gas and shear for fluid conditions thought to be satisfied over a wide range of radii in these discs.     

Kantowski–Sachs bulk viscous string cosmological model in Brans–Dicke theory of gravitation

This paper deals with the collapse and expansion of relativistic anisotropic self-gravitating source. The field equations for non-radiating and non-static plane symmetric anisotropic source have been evaluated. The non-radiating property of the fluid leads to evaluation of the metric functions. We have classified the dynamical behavior of gravitational source as expansion and collapse. The collapse in this case leads to the final stage without the formation of apparent horizons while such horizons exists in case of spherical anisotropic source. The matching of interior and exterior regions provides the continuity of masses over the boundary surface.