A self-similar solution for spherically symmetric gravitational collapse

A model of gas-dynamical flow during gravitational collapse is analyzed mathematically by assuming its spherical symmetry and self-similarity. A shock wave diverging from the center emerges in this model. The physical requirements imposed on the post-shock flow at the center for the specified parameters at infinity unambiguously determine the shock front and the flow behind it.     

Cosmic equation of state and advanced LIGO-type gravitational wave experiments

It is hoped that the future generation of interferometric gravitational wave detectors will provide accurate measurements of the final stages of binary in-spirals. The sources probed by such experiments are of extragalactic origin and the observed chirp mass is the intrinsic chirp mass multiplied by (1+ z ) where z is the redshift of the source. Moreover the luminosity distance is a direct observable in such experiments. This creates the possibility to establish a new kind of cosmological test, supplementary to more standard ones.
Recent observations of distant type Ia supernovae light curves suggest that the expansion of the Universe has recently begun to accelerate. A popular explanation of the present accelerating expansion of the Universe is to assume that some part Ω_Q of the matter–energy density is in the form of a dark component called 'the quintessence' with the equation of state p _Q= wρ _Q with w ≥−1 . In this paper we consider the predictions concerning observations of binary in-spirals in future LIGO-type interferometric experiments assuming a 'quintessence cosmology'. In particular we compute the expected redshift distributions of observed events in the a priori admissible range of parameters describing the equation of state for the quintessence. We find that this distribution has a robust dependence on the cosmic equation of state.     

A limit for gravitational collapse

Earlier, under certain simplifying assumptions, on the basis of the General Theory of Relativity, it has been concluded by many authors that when the radius of a gravitationally collapsing spherical object of massM reaches the critical value of the Scharzschild radiusR _s=2GM/c ², then, in a co-moving frame, the object collapses catastrophically to a point. However, in drawing this conclusion due consideration has not been given to the nuclear forces between the nucleons. In particular, the very strong ‘hard-core’ repulsive interaction between the nucleons which has the range ～0.4×10^?13 cm has been totally ignored. On taking into account this ‘hard-core’ repulsive interaction, it is found that no spherical object of massM g can collapse to a volume of radius smaller thanR _min=(1.68×10^?6)M ^1/3 cm or to a density larger than ρ_max=5.0 × 10¹⁶ g cm^?3. It has also been pointed out that objects of mass smaller thanM _c～1.21×10³³ g can not cross the Schwarzschild barrier and gravitationally collapse. The only course left to the objects of mass less thanM _cis to reach the equilibrium as either a white dwarf or a neutron star.     

Spin effects in gravitational collapse

We suggest that only slowly spinning stars undergoing gravitational collapse can eject their envelope in a supernova explosion and leave behind a remnant in the form of a neutron star or a pulsar. Faster spinning stars fail to explode and perhaps become black holes.Work supported in part by the National Science Foundation under Grant Nos PHY75-21591 and PHY76-11445.     

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.     

Homologous gravitational collapse in Lagrangian representation

The classical problem of spherical homologous gravitational collapse with a polytropic equation of state with γ=4/3 is examined in Lagrangian fluid coordinate. The fluid velocity v(t)=dr(t)/dt=ηdy/dt is derived from the evolution function y(t) where η=r(0) is the radial fluid label in Lagrangian formulation. The evolution function y(t), which describes the collapse time history of a finite pressure cloud, is solved which happens to be identical to the well established parametric form of Mestel (Mon. Not. R. Astron. Soc., 6:161–198, 1965) for cold cloud collapse. The spatial structure is described by a nonlinear equation of the density profile function q(z) with z=aη. Due to the nonlinearity, the collapse profile is highly non-uniform in space. For moderate values of q(0), the solutions are homologous. For large q(0), homology is broken leading to the formation of a central core and a central cavity. The stellar envelope bounding the central cavity collapses under the additional external gravity of the central core, generating eventually a sequence of cavity-shell structure in the envelope, until the entire mass of the original cloud is accounted for.     

Shock fragmentation model for gravitational collapse

A cloud of gas collapsing under gravity will fragment.We present a new theory for this process,in which layers of shocked gas fragment due to their gravitational instability.Our model explains why angular momentum does not inhibit the collapse process.The theory predicts that the fragmentation process produces objects which are significantly smaller than most stars,implying that accretion onto the fragments plays an essential role in determining the initial masses of stars.This prediction is also consistent...     

Radiating gravitational collapse with shear viscosity

A model is proposed of a collapsing radiating star consisting of an isotropic fluid with shear viscosity undergoing radial heat flow with outgoing radiation. The pressure of the star, at the beginning of the collapse, is isotropic but owing to the presence of the shear viscosity the pressure becomes more and more anisotropic. The behaviour of the density, pressure, mass, luminosity and the effective adiabatic index is analysed. Our work is compared to the case of a collapsing shearing fluid of a previous model, for a star with 6 M_⊙.     

Horizon-free gravitational collapse of radiating fluid sphere

In this paper we present a detailed study of BCT Ist solution Tewari (Astrophys. Space Sci. 149:233, 1988) representing time dependent balls of perfect fluid with matter-radiation in general relativity. Assuming the life time of quasar 10⁷ years our model has initial mass≈10⁸ M _Θ with an initial linear dimension≈10¹⁵ cm. Our model is radiating the energy at a constant rate i.e. L _∞=10⁴⁷ ergs/sec with the gravitational red shift, z=0.44637. In this model we have 2GM(u)/c ² R _S (u))=0.3191 i.e. the model is horizon free.     

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.     

Axisymmetric gravitational collapse of rotating interstellar gas clouds

Numerical calculations have been made of the gravitational axisymmetric collapse of isothermal gas clouds endowed with angular momentum. The evolutionary study is based on the so-called Fluid-in-Cell method coupled to an efficient algebraic algorithm which allows the Poisson equation to be integrated by means of block tri-diagonal matrices. The results, at ages slight larger than the initial free-fall time, indicate that flattened disk-shaped structures are formed in the central region of the clouds-in good agreement with the previous analytical results predicted by the authors.     

Problems on gravitational collapse of interstellar gas clouds

The gravitational collapse of a spherically symmetric interstellar gas cloud has been investigated following the non-linear discontinuity waves propagation theory. It has been pointed out that macroscopic phenomena, such as the process of fragmentation, can arise (shock wave formation)-even in the case of spherical symmetry- at times smaller than the free-fall timet _ff, provided the initial data of the Cauchy problem be discontinuous within a sphere of radius (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical timest _cr<t _ff (depending on the typical non-linear structure of the differential system). The cooling-heating function plays an important role in contrasting the formation of shock waves.     

On the integrability cases of the equation of motion for a satellite in an axially symmetric gravitational field

The projection of an axially symmetric satellite's orbit on a plane perpendicular to the rotation axis (z=const.) is given by the second-order differential equation. $$\frac{{y''}}{{1 + y'^2 }} = \bar \Psi _y - y'\bar \Psi _{x,}$$ where the prime denotes the derivative with respect tox and \(\bar \Psi (x,y)\) is a known function. Two integrability cases have been investigated and it has been shown that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the calssical plane eikonal equation of geometric optics.     

Radiating star,shear-free gravitational collapse without horizon

We present a new model of dissipative energy fluid without appearance of horizon. The interior matter fluid is shear-free isotropic spherically symmetric and undergoing radial heat flow. The interior metric is matched with Vaidya exterior metric over the boundary. The model obeyed all the relevant physical and thermodynamic conditions. In this model, the collapse begins at infinite past with both infinite mass and radius and contracts to a point as time tends to zero without forming an event horizon.     

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.     

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.