Related papers: Comment on: "Analytical approximations for the col…

The old suggestive observation that black holes often resemble lumps of fluid has recently been taken beyond the level of an analogy to a precise duality. We investigate aspects of this duality, and in particular clarify the relation…

We discover that a class of bubbles of nothing are embedded as time dependent scaling limits of previous spacelike-brane solutions. With the right initial conditions, a near-bubble solution can relax its expansion and open the compact…

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,…

This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken…

Motivated by the discovery of a plenitude of metastable vacua in a string landscape and the possibility of rapid tunneling between these vacua, we revisit the dynamics of a false vacuum bubble in a background de Sitter spacetime. We find…

We introduce Rayleigh functional for nonlinear systems. It is defined using the energy functional and the normalization properties of the variables of variation. The key property of the Rayleigh quotient for linear systems is preserved in…

We study Smoluchowski-Poisson equation in two space dimensions provided with Dirichlet boundary condition for the Poisson part. For this equation several profiles of blowup solution have been noticed. Here we show collapse mass quantization…

We prove a singularity theorem in semiclassical gravity without assuming global hyperbolicity or the null energy/curvature condition; the former is replaced by the weaker causality conditions of stable causality and past reflectivity, and…

We model the collapse of a spherically symmetric, constant density, pressureless shell onto a preexisting black hole. Contrary to a recent claim of Liu and Zhang (2009), we show that an observer at infinity never sees any part of the shell…

We explore numerically the evolution of a collapsing spherical shell of charged, massless scalar field. We obtain an external \RN space-time, and an inner space-time that is bounded by a singularity on the Cauchy Horizon. We compare these…

Nonlinear deformations of a two-dimensional gas bubble are investigated in the framework of a Hamiltonian formulation involving surface variables alone. The Dirichlet--Neumann operator is introduced to accomplish this dimensional reduction…

We analyze the mechanism that determines the boundary of stability in Taylor-Couette flow. By simple physical argument we derive an analytic expression to approximate the stability line for all radius ratios and all speed ratios, for co-…

The potential flow of an incompressible inviscid heavy fluid over a light one is considered. The integral version of the method of matched asymptotic expansion is applied to the construction of the solution over long intervals of time. The…

Results of investigation of the asymptotic behavior of solutions to the Cauchy problems for a quasi-linear parabolic equation with a small parameter at a higher derivative near singular points of limit solutions are presented. Interest to…

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…

We investigate the bounce solutions in vacuum decay problems. We show that it is possible to have a stable false vacuum in a potential that is unbounded from below.

We describe a simple method of determining whether the singularity that forms in the spherically symmetric collapse of inhomogeneous dust is naked or covered. This derivation considerably simplifies the analysis given in the earlier…

Generalizing earlier results of Joshi and Dwivedi (Commun. Math. Phys. 146, 333 (1992); Lett. Math. Phys. 27, 235 (1993)), we analyze here the spherically symmetric gravitational collapse of a matter cloud with a general form of matter for…

In this paper, we derive a sharp version of the singular Trudinger-Moser inequality, which was originally established by Adimurthi and Sandeep (Nonlinear Differ. Equ. Appl. 2007). Moreover, extremal functions for those singular…

We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…