Universality of the Buchdahl sphere

TL;DR

This paper explores universal properties of the Buchdahl sphere, demonstrating their invariance across charge, gravity theories, and rotation, and introduces a new Buchdahl limit for slowly-rotating stars.

Contribution

It uncovers universal characteristics of the Buchdahl sphere that remain consistent across different physical conditions and proposes a novel Buchdahl limit for rotating stellar objects.

Findings

Universal properties hold regardless of electric charge.

Universality extends to pure Lovelock gravity theories.

A new Buchdahl limit for slowly-rotating stars is proposed.

Abstract

Buchdahl sphere, the limiting stable isotropic stellar structure without exotic matter, plays a very important role in our understanding of how compact an astrophysical object can be. Here, we show certain universal properties associated with the Buchdahl sphere, in the sense that these properties will not change with the inclusion of electric charge in the stellar structure, or, will hold good in the pure Lovelock theories of gravity as well. Using these universalities, we have proposed a Buchdahl limit for a slowly-rotating stellar configuration, for the first time. Finally, the universality of the Buchdahl sphere in terms of the gravitational and non-gravitational field energies, as well as for the photon sphere have also been discussed.