Related papers: Structural stability and general relativity
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
Scalar-tensor~(ST) theories of gravity are natural phenomenological extensions to general relativity. Although these theories are severely constrained both by solar system experiments and by binary pulsar observations, a large set of ST…
We prove the instability of a ``critical'' solitary wave of the generalized Korteweg -- de Vries equation, the one with the speed at the border between the stability and instability regions. The instability mechanism involved is ``purely…
We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole -approaching a sub-extremal Reissner-Nordstr\"om background fast enough at infinity- in presence of a massive and charged…
An analysis of all known spherically symmetric solutions to the field equations originating from the Riemann tensor quadratic curvature Lagrangian is presented. A new exact solution is found for the field equation originating from the…
The addition of a Ricci coupling to Einstein-scalar-Gauss-Bonnet theories makes general relativity a cosmological attractor. Previous work considered a quadratic coupling function with two independent coupling constants in such theories and…
We discuss the constraints imposed on the nonlinear evolution of the Large Scale Structure (LSS) of the universe by galilean invariance, the symmetry relevant on subhorizon scales. Using Ward identities associated to the invariance, we…
In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the 1 + 3 dimensional Euler-Einstein system with a positive cosmological constant. These background…
This paper presents a proof of generic structural stability for Riemann solutions to $2 \times 2$ system of hyperbolic conservation laws in one spatial variable, without diffusive terms. This means that for almost every left and right…
We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
A thorough study and analysis on the conceptual foundations of unimodular gravity shows that this theory is essentially general relativity disguised as unimodular relativity in the literature. The main reason for this dilemma is accepting…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
Furstenberg--Zimmer structure theory refers to the extension of the dichotomy between the compact and weakly mixing parts of a measure preserving dynamical system and the algebraic and geometric descriptions of such parts to a conditional…
An open problem in general relativity has been to construct an asymptotically flat solution to a reasonable Einstein-matter system containing a black hole in the future and yet past-causally geodesically complete, in particular, containing…
We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved…