Related papers: Stability for the spherically symmetric Einstein-V…
We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field (HMF) model, a prototype for long-range interactions in $N$-particle dynamics. In particular, we point out the role played by the infinity of…
We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit…
It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for…
We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is non perturbative and contains a condensate of the metric tensor in a manner reminiscent of Yang-Mills theories. As a simple step toward the…
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…
We consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We prove a persistence result for such relative…
It is well known that steady states of the Vlasov-Poisson system, a widely used model in non-relativistic galactic dynamics, have negative energy. In this paper we derive the analogous property for two relativistic generalizations of the…
We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
We consider a massless, minimally coupled scalar with a quartic self-interaction which is released in Bunch-Davies vacuum in locally de Sitter background of an inflating universe. It was shown, in this system, that quantum effects can…
We use the canonical energy method of Hollands and Wald to study the stability properties of asymptotically flat, stationary solutions to a very general class of theories, consisting of a set of coupled scalar fields and p-form gauge…
We consider the asymptotically flat standing wave solutions to the Poisson-Schr\"{o}dinger system of equations known as static states. These solutions can be parameterized using a variety of choices of two continuous parameters and one…
This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov…
We discuss the asymptotic stability of stationary solutions to the incompressible Navier-Stokes equations on the whole space in Besov spaces with positive smoothness and low integrability. A critical estimate for the semigroup generated by…
The effects of the cosmological constant on the static equilibrium configurations and stability against small radial perturbations of relativistic polytropic spheres are investigated. This study numerically solves the hydrostatic…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…