On the equivalence of approximate stationary axially symmetric solutions of Einstein field equations
arXiv:1510.02035 · doi:10.1134/S0202289316040046
Abstract
We study stationary axially symmetric solutions of the Einstein vacuum field equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. We derive explicitly the exterior Sedrakyan-Chubaryan approximate solution, and express it in analytical form, which makes it practical in the context of astrophysical applications. In the limiting case of vanishing angular momentum, the solution reduces to the well-known Schwarzschild solution in vacuum. We demonstrate that the new solution is equivalent to the exterior Hartle-Thorne solution. We establish the mathematical equivalence between the Sedrakyan-Chubaryan, Fock-Abdildin and Hartle-Thorne formalisms.
8 pages
References in corpus (7)
- Effective No-Hair Relations for Neutron Stars and Quark Stars: Relativistic Results
- Relativistic models of magnetars: structure and deformations
- Gravitational field of compact objects in general relativity
- An all-purpose metric for the exterior of any kind of rotating neutron star
- Magnetic fields in anisotropic relativistic stars
- Slowly rotating fluid balls of Petrov type D
- The quadrupole moment of slowly rotating fluid balls