Related papers: Structural stability and general relativity
A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We consider the linearized semiclassical Einstein equations for small deviations around de Sitter spacetime including the vacuum polarization effects of conformal fields. Employing the method of order reduction, we find the exact solutions…
The singularity of the solutions obtained before in the teleparallel theory of gravitation is studied. Also the stability of these solutions is studied using the equations of geodesic deviation. The condition of stability is obtained. From…
The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…
We generalize the scalar tensor bigravity models to the non-minimal kinetic coupling scalar tensor bigravity models with two scalar fields whose kinetic terms are non-minimally coupled to two Einstein tensors constructed by two metrics. We…
We summarize some our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue…
The goal of this paper is to provide a geometric framework for analyzing the uniform decay properties of solutions to the Teukolsky equation in the fully nonlinear setting of perturbations of Kerr. It contains the first nonlinear version of…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
The stability of a special class of equilibria for the free rigid body on $\mathfrak{so}(5)$ is discussed. An instability region and two stability regions are established. The list of constants of motion which assure the complete…
We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two…
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…
We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced…
Topological stars are regular, horizonless solitons arising from dimensional compactification of Einstein-Maxwell theory in five dimensions, which could describe qualitative properties of microstate geometries for astrophysical black holes.…
In this paper, we study planar polygonal curves from the variational methods. We show an unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first…
The present paper investigates the structural stability of bidirectional cyclic negative feedback systems. To address this, we develop a generalized Floquet theory and construct nested invariant cones for the systems. Subsequently, we…
This article presents a comprehensive analysis of the formation and dissipation of vortices within chaotic fluid flows, leveraging the framework of Sobolev and Besov spaces on Riemannian manifolds. Building upon the Navier-Stokes equations,…
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr black hole spacetime. The estimates are valid for the full…
We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or…