Revisiting the Einstein field of a mass point

TL;DR

This paper derives the Einstein gravitational field of a point mass by taking a limit from a sphere of fluid, emphasizing that singularities are physically linked to matter presence.

Contribution

It provides a new derivation of the point mass field in general relativity using a limiting process from a fluid sphere, reinforcing the matter-singularity connection.

Findings

The point mass gravitational field is obtained as a limit of a fluid sphere's field.

Supports the view that singularities correspond to actual matter presence.

Clarifies the physical interpretation of singularities in Einstein's theory.

Abstract

The Einstein gravitational field of a material point at rest is derived anew - by a suitable limit process - from the field of a sphere of a homogeneous and incompressible fluid. This result supports clearly the thesis according to which the physically interesting singularities must correspond to the presence of matter in loco.