相关论文: Newtonian Stellar Models
We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space,…
In this paper, the gravitational field equations for static spherically symmetric perfect fluid models with a polytropic equation of state, $p=k\rho^{1+1/n}$, are recast into two complementary 3-dimensional {\it regular} systems of ordinary…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding…
We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the…
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These…
The aim of this paper is to discuss the theory of Newtonian and relativistic polytropes with generalized polytropic equation of state. For this purpose, we formulated the general framework to discuss the physical properties of polytrops…
For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the…
We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…
We investigate spherically symmetric equilibrium states of the Vlasov-Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations…
Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with…
The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order…
Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters---the…
A general formalism recently proposed to study Newtonian polytropes for anisotropic fluids is here extended to the relativistic regime. Thus, it is assumed that a polytropic equation of state is satisfied by, both, the radial and the…
We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of…
To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on…
We consider static neutron stars within the framework of $R^2$ gravity. The neutron fluid is described by three different types of realistic equations of state (soft, moderately stiff, and stiff). Using the observational data on the neutron…
We investigate the field equations in the Einstein-aether theory for static spherically symmetric spacetimes and a perfect fluid source and subsequently with the addition of a scalar field (with an exponential self-interacting potential).…