Related papers: Asymptotic silence-breaking singularities
In this paper we study the behavior of the scalar curvature at infinity on complete noncompact steady gradient Ricci solitons. In dimension four, we assume that the canonical Ricci flow induced by the soliton is a weak $\kappa$-solution and…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a `kinematic singularity' at which the fluid congruence is inextendible but…
In this lecture we will show some properties of a singularity-free solution to Einstein's equations and its accordance with some theorems dealing with singularities. We will also discuss the implications of the results.
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally…
The causal character of the zero-areal-radius (R=0) singularity in spherically symmetric spacetimes is studied. By using the techniques of the qualitative behaviour of dynamic systems, we are able to present the most comprehensive scheme so…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
We study a scalar field in curved space in three dimensions. We obtain a static perturbative solution and show that this solution satisfies the exact equations in the asymptotic region at infinity. The new solution gives rise to a…
We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cosmologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are…
We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a…
We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter $w=p/\rho$, there exist…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
We consider the asymptotic behaviour of positive solutions u of the conformal scalar curvature equation, \Delta u + n(n-2)/4 u^{(n+2)(n-2) = 0, in the neighbourhood of isolated singularities in the standard Euclidean ball. Although…
In this work we analyse asymptotically flat, spherically symmetric spacetimes in which an event horizon is present without any trapped surfaces. We identify two types of such spacetimes, each related to the asymptotic behaviour (in time) of…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that…
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with…
The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…