Related papers: On a weak solution of Einstein equations for expan…
We consider flat Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the…
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions.…
In case of spherical symmetry, the assumptions of finite-time formation of a trapped region and regularity of its boundary --- the apparent horizon --- are sufficient to identify the form of the metric and energy-momentum tensor in its…
A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
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 give two new analytical solutions to the low-energy string theory action that violate the weak cosmic censorship conjecture. They are classical charged solutions to the Einstein-Maxwell-dilaton theory in four dimensions that come in two…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms…
We consider the Navier-Stokes equations in a three-dimensional thin spherical shell and on the two-dimensional unit sphere, and estimate the difference of weak solutions on the thin spherical shell and the unit sphere. Assuming that the…
We will describe here the structure of singularity forming in gravitational collapse of spherically symmetric inhomogeneous dust. Such a collapse is described by the Tolman-Bondi-Lema{\^i}tre metric. The main new result here relates, in a…
We study the bulk viscosity taking dust matter in the generalized teleparallel gravity. We consider different dark energy models in this scenario along with a time dependent viscous model to construct the viscous equation of state parameter…
In a previous work we obtained exact solutions for the proper time quantum mechanics of a thin dust shell, collapsing in a vacuum. We extend these results to the quantum collapse of a dust shell surrounding a pre-existing black hole. In…
Thin-shell wormholes are constructed starting from the exotic branch of Wiltshire spherically symmetric solution of Einstein-Gauss-Bonnet gravity. The energy-momentum tensor of the shell is studied, and it is shown that configurations…
Exact solutions of Einstein equations with null Riemman-Christoffel curvature tensor everywhere, except on a hypersurface, are studied using quantum particles obeying the Klein-Gordon equation. We consider the particular cases when the…
In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out…
In a recent approach in modelling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasised. It is possible to generate a model which is physically reasonable by approximately solving the…
This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded…
We prove conditional weak-strong uniqueness of the potential Euler solution for external flow around a smooth body in three space dimensions, within the class of viscosity weak solutions with the same initial data. Our sufficient condition…
A simple and direct, based on the equations of motion, derivation of the variational principle and effective actions for a spherical charged dust shell in general relativity is offered. This principle is based on the relativistic version of…