Related papers: Existence for Stable Rotating Star-Planet Systems
In this paper we classify the free boundary associated to equilibrium configurations of compressible, self-gravitating fluid masses, rotating with constant angular velocity. The equilibrium configurations are all critical points of an…
It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its mass-to-radius ratio, $2M/R\leq 8/9$. However, field configurations typically will not be compact. Here…
We present a rigorous proof establishing the mathematical equivalence between two independent criteria for the marginal stability of multi-fluid relativistic stars: the dynamical criterion based on the vanishing of the fundamental radial…
The fundamental properties of low-mass stars are not as well understood as those of their more massive counterparts. The best method for constraining these properties, especially masses and radii, is to study eclipsing binary systems, but…
We reinvestigate the stability properties of ultracompact spinning boson stars with a stable light ring using fully nonlinear 3+1 and 2+1 numerical relativity simulations and two different formulations of the Einstein equations. We find no…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…
Recently, we have shown that dynamically stable ergostar solutions (equilibrium neutron stars that contain an ergoregion) with a compressible and causal equation of state exist [A. Tsokaros, M. Ruiz, L. Sun, S. L. Shapiro, and K. Ury\=u,…
We investigate the orbital stability of a putative Jovian planet in a compact binary \nu Octantis reported by Ramm et al. We re-analyzed published radial velocity data in terms of self-consistent Newtonian model and we found stable best-fit…
A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system.…
This paper is concerned with the existence and mass concentration behavior of minimizers for rotating Bose-Einstein condensations (BECs) with attractive interactions in a bounded domain $\mathcal{D}\subset \mathbb{R}^2$. It is shown that,…
We construct stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of polytropic gaseous stars, with small constant angular velocity when the adiabatic exponent $\gamma$ belongs to…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
Quasi-local variables, i.e. quantities whose values can be derived from physics accessible within an arbitrarily small neighborhood of a spacetime point, are used to construct the equation of state (EoS) for the anisotropic fluid in the…
We present a stability analysis of a large set of simulated planetary systems of three or more planets based on architectures of multiplanet systems discovered by \textit{Kepler} and \textit{K2}. We propagated 21,400 simulated planetary…
We construct spherically-symmetric static solutions of the Einstein-Klein-Gordon-Euler system involving a complex scalar field governed by a periodic potential which emerges in models of axion-like particles, and fermionic matter modeled by…
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…
Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been…
We present a stability result for ground states of a Schr\"odinger-Poisson system in $(2+1)$ dimension, modelling the propagation of a light beam through a liquid crystal with nonlocal nonlinear response. The core of the proof is a…
The binary star system gamma Cephei is unusual in that it harbours a stable giant planet around the larger star at a distance only about a tenth of that of the stellar separation. Numerical simulations are carried out into the stability of…
In this article, we study the multiplicity, asymptotics and stability of standing waves with prescribed mass $c>0$ for nonlinear Schr\"odinger equation with rotation in the mass-supercritical regime arising in Bose-Einstein condensation.…