An approximate global solution of Einstein's equations for a rotating two layers star

Abstract

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear equation of state moving in a rigid motion pattern. Using the post-Min\-kows\-kian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic coordinates. Interior and exterior solutions are matched, in the sense described by Lichnerowicz, on the surfaces of constant pressure, to obtain a global solution.

13 pages. arXiv admin note: substantial text overlap with arXiv:1702.05908

References in corpus (4)

• On the construction of global models describing rotating bodies; uniqueness of the exterior gravitational field
• An approximate global solution of Einstein's equations for a finite body
• An approximate global solution of Einstein's equation for a rotating compact source with linear equation of state
• An approximate global solution to the gravitational field of a perfect fluid in slow rotation