On slowly rotating axisymmetric solutions of the Einstein-Euler equations

Abstract

In recent works we have constructed axisymmetric solutions to the Euler-Poisson equations which give mathematical models of slowly uniformly rotating gaseous stars. We try to extend this result to the study of solutions of the Einstein-Euler equations in the framework of the general theory of relativity. Although many interesting studies have been done about axisymmetric metric in the general theory of relativity, they are restricted to the region of the vacuum. Mathematically rigorous existence theorem of the axisymmetric interior solutions of the stationary metric corresponding to the energy-momentum tensor of the perfect fluid with non-zero pressure may be not yet established until now except only one found in the pioneering work by U. Heilig done in 1993. In this article, along a different approach to that of Heilig's work, axisymmetric stationary solutions of the Einstein-Euler equations are constructed near those of the Euler-Poisson equations when the speed of light is sufficiently large in the considered system of units, or, when the gravitational field is sufficiently weak.

References in corpus (7)

• On slowly rotating axisymmetric solutions of the Euler-Poisson equations
• The Newtonian limit for perfect fluids
• On Rotating Axisymmetric Solutions of the Euler-Poisson Equations
• Post-Newtonian expansions for perfect fluids
• Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order
• Existence of families of spacetimes with a Newtonian limit
• Second order perturbations of rotating bodies in equilibrium; the exterior vacuum problem

Cited by in corpus (6)

• Recent developments in mathematical aspects of relativistic fluids
• The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion
• Existence and uniqueness of compact rotating configurations in GR in second order perturbation theory
• A Remark on the Matter-Vacuum Matching Problem for Axisymmetric Metrics Governed by the Einstein-Euler Equations
• On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary
• A Note on the Axisymmetric Stationary Metric in the General Theory of Relativity