Related papers: Nonlinear Shear-free Radiative Collapse
We study the gravitational collapse of a spherically symmetric anisotropic relativistic star within Einstein theory of gravity making use of one of our recently developed collapsing stellar models [{\it Astrophys. Space Sci.} {\bf361} 99…
We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure…
We are interested in the following semilinear elliptic problem: \begin{equation*} \begin{cases} -\Delta u + \lambda u = u^{p-1} \ \text{in} \ T,\\ u > 0, u = 0 \ \text{on} \ \partial T,\\ \int_{T}u^{2} \, dx= c \end{cases} \end{equation*}…
We study the nonlinear radial stability of boson stars with a solitonic potential across the entire parameter space, focusing especially on families of solutions that support ultracompact models on the perturbatively stable branch. Using a…
We construct new models of black hole-neutron star binaries in quasiequilibrium circular orbits by solving Einstein's constraint equations in the conformal thin-sandwich decomposition together with the relativistic equations of…
Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
We consider the question of scattering for the boson star equation in three space dimensions. This is a semi-relativistic Klein-Gordon equation with a cubic nonlinearity of Hartree type. We combine weighted estimates, obtained by exploiting…
We analyze the problem of gravitational collapse considering the matching of an exterior region described by the Vaidya's metric and an interior region described by a spherically symmetric shear-free inhomogeneous geometry sourced by a…
We model the gravitational collapse of heavy massive shells including its main quantum corrections. Among these corrections, quantum improvements coming from Quantum Einstein Gravity are taken into account, which provides us with an…
The merger remnant of a binary neutron star coalescence is initially strongly differentially rotating. Some properties of these remnants can be accurately modeled through building equilibrium neutron star models. In the present paper, we…
We construct smooth static bubble solutions, denoted as topological stars, in five-dimensional Einstein-Maxwell theories which are asymptotic to $\mathbb{R}^{1,3}\times$S$^1$. The bubbles are supported by allowing electromagnetic fluxes to…
In this work we explore the effects of nonlinearity on three-dimensional topological phases. Of particular interest are the so-called Weyl semimetals, known for their Weyl nodes, i.e., point-like topological charges which always exist in…
We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We…
We investigate the fate of a collapsing stellar core, which is the final state of evolution of a massive, rotating star of a Wolf-Rayet type. Such stars explode as type I b/c supernovae, which have been observed in association with long…
We study the semilinear elliptic system \[ \Delta u = p(|x|)\,g(v), \qquad \Delta v = q(|x|)\,f(u), \qquad x \in \mathbb{R}^n,\; n \geq 3, \] under new Keller--Osserman-type integral conditions on the nonlinearities $f,g$ and decay…
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…
We discuss the stability and construct dynamical configurations describing the gravitational collapse of unstable neutron stars with realistic equations of state compatible with the recent LIGO-Virgo constraints. Unlike other works that…
We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in…
We explore whether observed molecular clouds could include a substantial population of unbound clouds. Using simulations which include only turbulence and gravity, we are able to match observed relations and naturally reproduce the observed…