Einstein's Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid

TL;DR

This paper derives a system of six PDEs from Einstein's field equations to describe the interior of a uniformly rotating, axisymmetric perfect fluid, simplifying the complex gravitational equations for such systems.

Contribution

It reduces Einstein's equations to a manageable set of six PDEs specifically for rotating perfect fluid interiors, clarifying the mathematical structure of these models.

Findings

Six second order PDEs formulated for the interior of rotating fluids.

Four PDEs independent of pressure and density, two determine these quantities.

Provides a foundation for further analytical or numerical solutions.

Abstract

We reduce Einstein's field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density $\mu$ and four dependent variables.Four of these equations do not depend on p and $\mu$ and the other two determine p and $\mu$.