Related papers: Recollapsing spacetimes with $\Lambda<0$
Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their…
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…
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak…
For general gravitational collapse, inside the black-hole region, singularities $(r=0)$ may arise. In this article, we aim to answer how strong these singularities could be. We analyse the behaviours of various geometric quantities. In…
Global existence results in the past time direction of cosmological models with collisionless matter and a massless scalar field are presented. It is shown that the singularity is crushing and that the Kretschmann scalar diverges uniformly…
Critical collapse of a massless scalar field in spherical symmetry is systematically studied. We combine numerical simulations and asymptotic analysis, and synthesize critical collapse, spacetime singularities, and complex science. First…
We construct a three-dimensional, fully relativistic numerical model of a universe filled with an inhomogeneous pressureless fluid, starting from initial data that represent a perturbation of the Einstein-de Sitter model. We then measure…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions…
We study the backwards-in-time stability of the Schwarzschild singularity from a dynamical PDE point of view. More precisely, considering a spacelike hypersurface $\Sigma_0$ in the interior of the black hole region, tangent to the singular…
Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through…
Several classes of conformally-flat and spherically symmetric exact solutions to the Einstein field equations coupled with either a massless scalar field or a radiation fluid are given, and their main properties are studied. It is found…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…
We consider the wave equation, $\square_g\psi=0$, in fixed flat Friedmann-Lema\^itre-Robertson-Walker and Kasner spacetimes with topology $\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for solutions to the wave equation…
We investigate the dynamics of homogeneous gravitational collapse of a massless vector field in the presence of a positive cosmological constant $\Lambda$. The corresponding density function $\rho (a)$ obtained for the massless vector field…
We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of…
This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
Since horizon formation in global anti-de Sitter spacetime is dual to thermalization of a conformal field theory on a compact space, whether generic initial data is stable or unstable against gravitational collapse is of great interest. We…
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…
We consider the inhomogeneous Landau equation with $\gamma \in (\sqrt{3},2]$ and construct smooth, strictly positive initial data that develop a finite time singularity. The $C^{\alpha}$-norm of the distribution function blows up for every…