In this paper, the gravitational collapse of spherical interstellar clouds is discussed based on hydrodynamical simulations. The evolution is divided into two phases: former runaway collapse phase, in which the central density increases greatly on a nite time scale, and later contraction, associated with accretion onto a newborn star. The initial density distribution is expressed using a ratio ...

We present here a simple model of radiative gravitational collapse with radial heat flux which describes qualitatively the stages close to the formation of a superdense cold star. Starting with a static general solution for a cold star, the model can generate solutions for the earlier evolutionary stages. The temporal evolution of the model is specified by solving the junction conditions approp...

We investigate a spherical collapse model with and without the spatial curvature. We obtain the exact solutions of dynamical quantities such as the ratio of the scale factor to its value at the turnaround epoch (x ≡ a ata ) and the ratio of the overdensity radius to its value at the turnaround time (y ≡ R Rta ) with general cosmological parameters. The exact solutions of the overdensity at the ...

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of singular null geodesics to existence of regular curves which are super-solutions of the radial null geodesic equation, and allows us to treat all the known exampl...

In this work, we study the formation and evolution of dark matter halos by means of the spherical infall model with shell-crossing. We present a framework to tackle this effect properly, that does not involve the adiabatic approximation, and is based on the numerical follow-up, with time, of that individual shell of matter that contains always the same fraction of mass with respect to the total...

Under special conditions bacteria excrete an attractant and aggregate. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a theoretical description of the process, from the structure of the collapsing cylinder to the spacing of the final aggregates. We show that cylindrical collapse ...

By using the most general form of Einstein equations for General Relativistic (GTR) spherical collapse of an isolated fluid having arbitrary equation of state and radiation transport properties, we show that they obey a Global Constraint, 2GM(r, t)/R(r, t)c2 ≤ 1, where R is the “invariant circumference radius”, t is the comoving time, and M(r, t) is the gravitational mass enclosed within a como...

Gravitational collapse is one of the most important problem in classical general relativity. Usually, the formation of compact stellar objects such as white dwarf and neutron star are preceded by a period of collapse. Hence for astrophysical collapse, it is necessary to describe the appropriate geometry of interior and exterior regions and to determine proper junction conditions which allow the...

By means of N-body simulations, we study the evolution of gravity-dominated systems from an early relaxation to a collapse, focusing on the velocity distributions and thermodynamic properties. To simulate the dynamical evolution, we consider self-gravitating small N-body systems enclosed in a spherical container with adiabatic or semipermeable walls. It is demonstrated that in the early relaxat...

We solve the nonlinear evolution of pressureless, irrotational density fluctuations in a perturbed Robertson-Walker spacetime using a new Lagrangian method based on the velocity gradient and gravity gradient tensors. Borrowing results from general relativity, we obtain a set of Newtonian ordinary differential equations for these quantities following a given mass element. Using these Lagrangian ...