Related papers: A framework for perturbations and stability of dif…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
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 present new results on instabilities in rapidly and differentially rotating neutron stars. We model the stars in full general relativity and describe the stellar matter adopting a cold realistic equation of state based on the unified SLy…
An understanding of the dynamics of differentially rotating systems is key to many areas of astrophysics. We investigate the oscillations of a simple system exhibiting differential rotation, and discuss issues concerning the role of…
The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems which have in recent years been obtained by Yan Guo and the author in the context…
We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable…
We establish a nonlinear instability of the Euler-Poisson system for polytropic gases whose adiabatic exponents take value in $6/5<\gamma<4/3$ around the Lane-Emden equilibrium star configurations.
In this review, I discuss just three aspects of the stability and evolution of galactic discs. (1) I first review our understanding of the bar instability and how it can be controlled. Disc galaxies in which the orbital speed does not…
Path equations of different orbiting objects in the presence of very strong gravitational fields are essential to examine the impact of its gravitational effect on the stability of each system. Implementing an analogous method, used to…
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…
We demonstrate how observables of slowly rotating neutron stars can be used to constrain the nuclear equation of state. By building a Bayesian framework we demonstrate how combining different types of neutron star measurements, motivated by…
We study the stability of neutron stars with toroidal magnetic fields by magnetohydrodynamic simulation in full general relativity under assumption of axial symmetry. Nonrotating and rigidly rotating neutron stars are prepared for a variety…
The stability of static uncharged spheres with anisotropic internal stresses is studied in general relativity. It has been noticed that pressure anisotropy plays an important role for stability of stellar structure. It is shown that radial…
We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of…
In this paper, we have continued the work of Herrera \emph{et al.} \cite{herrera2012dynamical} in $f(G)$ gravitational theory. For this purpose, a spherically symmetric fluid exhibiting locally anisotropic pressure along with the energy…
Neutron stars provide an excellent laboratory for physics under the most extreme conditions. Up to now, models of axisymmetric, stationary, differentially rotating neutron stars were constructed under the strong assumption of barotropicity,…
At second order in perturbation theory, the $r$-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation-reaction, the…
We investigate the stability of self-gravitating spherically symmetric anisotropic spheres under radial perturbations. We consider both the Newtonian and the full general-relativistic perturbation treatment. In the general-relativistic…