Related papers: Type II critical collapse on a single fixed grid: …
For a zero-temperature Landau symmetry breaking transition in $n$-dimensional space that completely breaks a finite symmetry $G$, the critical point at the transition has the symmetry $G$. In this paper, we show that the critical point also…
We construct analytical models to study the critical phenomena in gravitational collapse of the Husain-Martinez-Nunez massless scalar field. We first use the cut-and-paste technique to match the conformally flat solution ($c=0$ ) onto an…
We investigate numerically the critical behaviour which occurs in the collapse of both spherically symmetric and asymmetric scalar field bubbles with full general relativity. We use a minimally coupled scalar field subject to a "double…
Solutions to the Einstein equations near the threshold of black hole formation exhibit remarkable behavior known as critical phenomena gravitational collapse. In this work we perform characteristic evolution in compactified Bondi…
In this paper, we investigate the Cauchy problem of the parabolic-parabolic Keller-Segel system with the logistic-type term $au-bu^\gamma$ on $\mathbb{R}^N, N\geq2$. We discuss the global boundedness of classical solutions with nonnegative…
The singularity structure of charged spherical collapse is studied by considering the evolution of the gravity-scalar field system. A detailed examination of the geometry at late times strongly suggests the validity of the mass-inflation…
Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…
We propose a method for numerical relativity in which the spatial grid is finite and no outer boundary condition is needed. As a "proof of concept" we implement this method for the case of a self-gravitating, spherically symmetric scalar…
We study a class of Hamiltonian deformations of the massless Einstein-Klein-Gordon system in spherical symmetry for which the Dirac constraint algebra closes. The system may be regarded as providing effective equations for quantum…
We study the inner-structure of a charged black-hole which is formed from the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent…
A convenient approach to analyze spatial infinity is to use a cylinder representation $I$ and impose a gauge based on a congruence of conformal geodesics. This so-called conformal Gauss gauge comes along with the freedom to specify initial…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
The weak cosmic censorship hypothesis can be understood as a statement that there exists a global Cauchy evolution of a selfgravitating system outside an event horizon. The resulting Cauchy problem has a free null-like inner boundary. We…
We present a thermodynamic analysis of spherically symmetric gravitational collapse. Using the Hayward-Kodama formalism, we treat a collapsing sphere as a thermodynamic system and express the surface gravity $\kappa_{hk}$ in terms of the…
We investigate critical phenomena during the gravitational collapse of a massive scalar field under two distinct semi-classical loop quantum gravity (LQG) approaches within spherical symmetry. Numerical simulations reveal that the massive…
We describe a formalism for studying spherically symmetric collapse of the massless scalar field in any spacetime dimension, and for any value of the cosmological constant $\Lambda$. The formalism is used for numerical simulations of…
Critical collapse of a spherically symmetric domain wall is investigated. The domain wall is made of a minimally coupled scalar field with a double well potential. We consider a sequence of the initial data which describe a momentarily…
We study the threshold of gravitational collapse in spherically symmetric spacetimes governed by the Einstein-Maxwell-Vlasov equations. We numerically construct solutions describing a collapsing distribution of charged matter that either…
We improve and extend Shapiro's model of a relativistic, compact object which is stable in isolation but is driven dynamically unstable by the tidal field of a binary companion. Our compact object consists of a dense swarm of test particles…
Analytical tools are extremely hard to find for non-linear gravitational collpase. Only a few simple but powerful tools exist so far. Two examples are the spherical collapse model (SCM) and stable clustering hypothesis (SCH). We present a…