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A fundamental open problem in the theory of the compressible Navier-Stokes equations is whether regular spherically symmetric flows can develop singularities, such as cavitation or implosion, in finite time. A formidable challenge lies in…
We investigate the gravitational collapse of a massive scalar field in a conformally flat, spherically symmetric spacetime within general relativity. The collapsing matter distribution is modeled using a minimally coupled homogeneous scalar…
In this paper, we examine gravitational collapse of matter fields in $n$-dimensional general relativity. The matter energy-momentum tensor under consideration includes dust, perfect fluids with equations of state and matter admitting bulk…
The gravitational collapse of a star is a warmly discussed but still puzzling problem, which not only involves the dynamics of the gases, but also the subtle coordinate transformation. In this letter, we give some more detailed…
We study the occurrence of naked singularities in the spherically symmetric collapse of radiation shells in a higher dimensional spacetime. The necessary conditions for the formation of a naked singularity or a black hole are obtained. The…
We examine the existence of an apparent horizon in the collapse of an isolated dust cloud using expansion functions. Our results indicate that in the region of spacetime far away from the gravitational singularity, the considered system has…
We review the status of the weak cosmic censorship conjecture, which asserts, in essence, that all singularities of gravitational collapse are hidden within black holes. Although little progress has been made toward a general proof (or…
In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric $f(R)$ gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the…
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…
The present analytical understanding on the nature of the singularities which form at the endstate of gravitational collapse of massive fluid bodies ("stars") is reviewed. Special emphasis is devoted to the issue of physical reasonability…
The closed-universe recollapse conjecture is studied for a class of closed spherically symmetric spacetimes which includes those having as a matter source: (1) a massless scalar field; (2) a perfect fluid obeying the equation of state $\rho…
Cold collapse of a cluster composed of small identical clumps, each of which is in virial equilibrium, is considered. Since the clumps have no relative motion with respect to each other initially, the cluster collapses by its gravity. At…
In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
The present paper deals with the gravitational collapse of an inhomogeneous spherical star consisting of dust fluid in the background of dark energy components with linear equation of state. We discussed the development of apparent horizon…
We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field.…
The role of the Raychaudhuri equation in studying gravitational collapse is discussed. A self-similar distribution of a scalar field along with an imperfect fluid in a conformally flat spacetime is considered for the purpose. The general…
Matter collapsing to a singularity in a gravitational field is still an intriguing question. Similar situation arises when discussing the very early universe or a universe recollapsing to a singularity. It is suggested that inclusion of…
We study the gravitational collapse in ($n+2$)-D quasi-spherical Szekeres space-time (which possess no killing vectors) with dust as the matter distribution. Instead of choosing the radial coordinate `$r$' as the initial value for the scale…
Quadratic Gravity supplements the Einstein-Hilbert action by terms quadratic in the spacetime curvature. This leads to a rich phase space of static, compact gravitating objects including the Schwarzschild black hole, wormholes, and naked…