On the equivalence of approximate stationary axially symmetric solutions of Einstein field equations

TL;DR

This paper derives and analyzes an approximate stationary axially symmetric solution to Einstein's vacuum equations, demonstrating its equivalence to known solutions and its applicability to modeling astrophysical objects.

Contribution

It explicitly derives the Sedrakyan-Chubaryan solution in analytical form and proves its equivalence to the Hartle-Thorne and other formalisms.

Findings

Sedrakyan-Chubaryan solution reduces to Schwarzschild when rotation vanishes

The new solution is mathematically equivalent to Hartle-Thorne formalism

Analytical form enhances practical astrophysical modeling

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.