Poisson type relativistic perfect fluid spheres
arXiv:1812.04958 · doi:10.1140/epjp/s13360-020-00948-x
Abstract
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 three simple examples based on the potential-density pairs corresponding to a harmonic oscillator (homogeneous sphere), the well-known Plummer model and a massive spherical dark matter halo model with a logarithmic potential. Moreover, the geodesic circular motion of test particles around such structures is studied. The stability of the orbits against radial perturbations is also analyzed using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models considered satisfy all the energy conditions.
arXiv comment10 pages, 11 figures
References in corpus (13)
- The Structure of Cold Dark Matter Halos
- Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations
- A Family of Models for Spherical Stellar Systems
- Dark Matter in Dwarf Spheroidals I: Models
- Rotation Curve and Mass Distribution in the Galaxy from the Velocities of Objects at Distances up to 200 kpc
- On the Stability of Circular Orbits of Particles Moving around Black Holes Surrounded by Axially Symmetric Structures
- Analytical families of 2-component anisotropic polytropes and their relativistic extensions
- A general relativistic approach to the Navarro-Frenk-White (NFW) galactic halos
- Parameters of Three Selected Model Galactic Potentials Based on the Velocities of Objects at Distances up to 200 kpc
- Newtonian and General Relativistic Models of Spherical Shells
- Newtonian and General Relativistic Models of Spherical Shells - II
- Models of spherical shells as sources of Majumdar-Papapetrou type spacetimes
- Three-dimensional axisymmetric sources for Majumdar-Papapetrou type spacetimes