Related papers: Initial value formalism for dust collapse
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
The Alcubierre metric is a spacetime geometry where a massive particle inside a spacetime distortion, called warp bubble, is able to travel at velocities arbitrarily higher than the velocity of light, a feature known as the warp drive. This…
We consider a one-dimensional system of particles, moving at constant velocities chosen independently according to a symmetric distribution on $\{-1,0,+1\}$, and annihilating upon collision -- with, in case of triple collision, a uniformly…
We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is…
We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not-necessarily small. Key to our argument is a form of quasilinear null…
The $3+1$ formalism provides a structured approach to analyzing spacetime by separating it into spatial and temporal components. When applied to the Robertson-Walker metric, it simplifies the analysis of cosmological evolution by dividing…
We consider the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, or more generally, in a gauge where the mean curvature of a timelike foliation is fixed near the boundary. We prove the existence of…
Effective dust collapse inspired by loop quantum gravity predicts two main features for general realistic initial profiles: a quantum gravitational bounce of the stellar core, when the energy density becomes planckian, and shell-crossing…
I present the first analytical study of gravitational collapse in a compact CMC foliation with $S^3$ spatial topology. The solutions I find, in this context, will be both solutions of Shape Dynamics and General Relativity. The aim is to…
We numerically study the dynamics of an imploding hollow cylinder composed of dust. Since there is no cylindrical black hole in 4-dimensional spacetime with physically reasonable energy conditions, a collapsed dust cylinder involves a naked…
We study an initial boundary value problem on a ball for the heat-conductive system of compressible Navier-Stokes-Fourier equations, in particular, a criterion of breakdown of the classical solution. For smooth initial data away from…
Through full solvability of 2+1 dimensional general relativity we derive out exact dynamic inner metric of collapsing stars with inhomogeneous initial mass distribution but joining with outside Anti-deSitt-Schwarzschild black holes…
We present in this paper the formalism for the splitting of a four-dimensional Lorentzian manifold by a set of time-like integral curves. Introducing the geometrical tensors characterizing the local spatial frames induced by the congruence…
We investigate a class of cylindrically symmetric inhomogeneous $\Lambda$-dust spacetimes which have a regular axis and some zero expansion component. For $\Lambda\ne 0$, we obtain new exact solutions to the Einstein equations and show that…
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…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
We have conducted a revised analysis of the first-order phase transition that is associated with symmetry breaking in a classically scale-invariant model that has been extended with a new $SU(2)$ gauge group. By incorporating recent…
The gravitational collapse of collisionless matter leads to shell-crossing singularities that challenge the applicability of standard perturbation theory. Here, we present the first fully perturbative approach in three dimensions by using…
The present paper is the first in a series that addresses the calculation of the full one-loop corrections of dark matter (DM) annihilation cross-sections in the low mass region of the inert doublet model (IDM). We first review the…
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…