A source of a quasi--spherical space--time: The case for the M--Q solution

TL;DR

This paper proposes a physically reasonable source for a static, axially symmetric solution to Einstein's equations, describing a quadrupole correction to Schwarzschild, useful for studying quasi-spherical gravitational fields.

Contribution

It introduces a new physically plausible source for a specific Weyl solution with quadrupole correction, enhancing understanding of quasi-spherical spacetime structures.

Findings

Supports the physical plausibility of the source

Shows the exterior spacetime is suitable for quasi-spherical fields

Provides arguments for the solution's relevance in gravitational studies

Abstract

We present a physically reasonable source for an static, axially--symmetric solution to the Einstein equations. Arguments are provided, supporting our belief that the exterior space--time produced by such source, describing a quadrupole correction to the Schwarzschild metric, is particularly suitable (among known solutions of the Weyl family) for discussing the properties of quasi--spherical gravitational fields.