Related papers: Variational Principle for Stars with a Phase Trans…
In this second article of a series we propose to base criteria of stability on the hamiltonian functional that is provided by the variational principle, to replace the reliance that has often been placed on {\it ad hoc} definitions of the…
The four equations of stellar structure are reformulated as two alternate pairs of variational principles. Different thermodynamic representations lead to the same hydromechanical equations, but the thermal equations require, not the…
We present a variational formalism for describing the dynamical evolution of an oscillating star with a point-mass companion in the linear, non-relativistic regime. This includes both the excitation of normal modes and the back-reaction of…
We study compact stars with hybrid equations of state consisting of a nuclear outer region and two nested quark phases, each separated from the lower density phase by a strong first-order phase transition. The stability of these models is…
The stability of hybrid stars with first-order phase transitions as determined by calculating fundamental radial oscillation modes is known to differ from the predictions of the widely-used Bardeen--Thorne--Meltzer criterion. We consider…
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results precisely…
Astrophysical observations of neutron stars probe the structure of dense nuclear matter and have the potential to reveal phase transitions at high densities. Most recent analyses are based on parametrized models of the equation of state…
In this paper a neutron star with an inner core which undergoes a phase transition, which is characterized by conformal degrees of freedom on the phase boundary, is considered. Typical cases of such a phase transition are e.g. quantum Hall…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
We study how the nature of a hybrid system (perfect fluid, solid or a mixture of them) could be related to the induction of general relativistic surface degrees of freedom on phase-splitting surfaces upon perturbation of its phases. We work…
Motivated by the possible existence of other universes, with possible variations in the laws of physics, this paper explores the parameter space of fundamental constants that allows for the existence of stars. To make this problem…
Matter interacts through two long range forces: gravity and electromagnetism. While all matter contributes to the gravitational potential, electromagnetic effects were traditionally expected to cancel in large systems because positive and…
We formulate within a generalized distributional approach the treatment of the stability against radial perturbations for both neutral and charged stratified stars in Newtonian and Einstein's gravity. We obtain from this approach the…
Two-imcompressible phase model of star is briefly revised. Effects of rotation and general relativity are considered.
Various theoretical arguments motivate an expectation of a phase transition in matter at extreme densities above nuclear density, accompanied by hopes that gravitational wave observations may reveal the properties of such a transition.…
We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients…
We study the dynamical stability and fates of hierarchical (in semi-major axis) two-planet systems with arbitrary eccentricities and mutual inclinations. We run a large number of long-term numerical integrations and use the Support Vector…
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…
The internal composition of neutron stars is still an open issue in astrophysics. Their innermost regions are impervious to light propagation and gravitational waves mostly carry global aspects of stars, meaning that only indirect…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…