On the stability of the objects of limiting compactness: Black hole and Buchdahl star

TL;DR

This paper demonstrates that black holes and Buchdahl stars, objects of limiting compactness in General Relativity, are inherently stable against various perturbations due to their gravitational energy properties.

Contribution

It provides a simple, general proof of the stability of these limiting compact objects, regardless of perturbation type, based on their gravitational energy characteristics.

Findings

Black holes and Buchdahl stars are stable objects of limiting compactness.

Their stability is independent of the nature of perturbations.

Gravitational energy equal to or half the mass underpins their stability.

Abstract

In General Relativity, there exist two objects of limiting compactness, one with a null boundary defining the horizon of a black hole and the other with a timelike boundary defining a Buchdahl star. The two are characterized by gravitational energy equal to or half the mass. Since non-gravitational mass-energy is the source of gravitational energy, both of these objects are manifestly stable. We demonstrate in this letter, in a simple and general way, that the equilibrium state defining the object is indeed stable, independent of the nature of the perturbation.