Non-spherical sources of static gravitational fields: investigating the boundaries of the no-hair theorem

TL;DR

This paper introduces a new static, non-spherical gravitational model using the gamma metric, exploring the behavior of naked singularities and the black hole limit within General Relativity.

Contribution

It presents a globally regular, non-spherical gravitating model satisfying physical conditions, advancing understanding of no-hair theorem boundaries.

Findings

The model satisfies energy, matching, and regularity conditions.

It provides insights into the directional behavior of naked singularities.

The model explores the Schwarzschild black hole limit.

Abstract

A new, globally regular model describing a static, non spherical gravitating object in General Relativity is presented. The model is composed by a vacuum Weyl--Levi-Civita special field - the so called gamma metric - generated by a regular static distribution of mass-energy. Standard requirements of physical reasonableness such as, energy, matching and regularity conditions are satisfied. The model is used as a toy in investigating various issues related to the directional behavior of naked singularities in static spacetimes and the blackhole (Schwarschild) limit.