Second-Order Pulsations In Polytropes

Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation

We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformally flat threemetric. We compare the results of our simulations, in which the spacetime dynamics is coupled to the evolution of the fluid, to previous results performed in the Cowling approximation in which the spacetime dynamics was neglec...

Iterative Nonlinear Pulsations in Massive Stars. II. Terms up to Second Order

The quasi-incompressible planet: some analytics

Exact and approximate analytical formulas are derived for the internal structure and global parameters of the spherical non-rotating quasi-incompressible planet. The planet is modeled by a polytrope with a small polytropic index n ≪ 1, and solutions of the relevant differential equations are obtained analytically, to the second order of n. Some solved and unsolved problems of polytropic models ...

Evolution of Relativistic Polytropes in the PostQuasiStatic Regime

A recently presented method for the study of evolving self-gravitating relativistic spheres is applied to the description of the evolution of relativistic polytropes. Two different definitions of relativistic polytrope, yielding the same Newtonian limit, are considered. Some examples are explicitly worked out, describing collapsing polytropes and bringing out the differences between both types ...

Uniformly Rotating Polytropic Rings in Newtonian Gravity

An iterative method is presented for solving the problem of a uniformly rotating, selfgravitating ring without a central body in Newtonian gravity by expanding about the thin ring limit. Using this method, a simple formula relating mass to the integrated pressure is derived to the leading order for a general equation of state. For polytropes with the index n = 1, analytic coefficients of the it...