Related papers: Gravitational collapse and the Vlasov-Poisson syst…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
Theory and simulations are used to study collisionless relaxation of a gravitational $N$-body system. It is shown that when the initial one particle distribution function satisfies the virial condition -- potential energy is minus twice the…
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
In the present work, we revisit the process of gravitational collapse of a spherically symmetric homogeneous dust fluid which is known as the Oppenheimer-Snyder (OS) model [1]. We show that such a scenario would not end in a spacetime…
A massless scalar field minimally coupled to the gravitational field in a simplified spherical symmetry is discussed. It is shown that, in this case, the solution found by Roberts, describing a scalar field collapse, is in fact the most…
The Nordstr\"om-Vlasov system describes the evolution of self-gravitating collisionless matter in the framework of a relativistic scalar theory of gravitation. We prove global existence and uniqueness of classical solutions for the…
We study spherically symmetric gravitational collapse of a homogeneous perfect fluid in Rastall gravity. Considering a linear equation of state (EoS) for the fluid profiles, we examine the conditions under which the collapse scenario could…
We develop here a new procedure within Einstein's theory of gravity to generate equilibrium configurations that result as the final state of gravitational collapse from regular initial conditions. As a simplification, we assume that the…
The supernovae are typical complex phenomena in fluid mechanics with very different time scales. We describe them in the light of catastrophe theory, assuming that successive equilibria between pressure and gravity present a saddle-node…
The Nordstr\"om-Vlasov system provides an interesting relativistic generalization of the Vlasov-Poisson system in the gravitational case, even though there is no direct physical application. The study of this model will probably lead to a…
We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure $p$ and density $\rho$ are related by the following relations (i) $p=k\rho$, (ii) $p=k\rho-\frac{B(v)}{\rho^{\alpha}}$ (variable modified…
We consider the gravitational clustering of a multicomponent fluid in an expanding Newtonian universe, taking into account the mutual gravitational interactions of the medium. We obtain a set of exact and approximate solutions for two fluid…
The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric fluid under the additional assumption that it is incompressible and stratified. In this setting we show that the…
The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…
Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a…
Recent developments on the final state of a gravitationally collapsing massive matter cloud are summarized and reviewed here. After a brief background on the problem, we point out how the black hole and naked singularity end states arise…
The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this…
We search for self-gravitating oscillating field lumps (pulsons) in the scalar model with logarithmic potential. With the use of a Krylov-Bogoliubov-type asymptotic expansion in the gravitational constant, the pulson solutions of the…
We review a recently proposed definition of complexity of the structure of self--gravitating fluids \cite{ch1}, and the criterium to define the simplest mode of their evolution. We analyze the origin of these concepts and their possible…