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

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.

14 Pages; Comments are Welcome. (Note: Prof. Naresh Dadhich passed away on the 6th of November, 2025. The whole idea and calculations were thoroughly discussed among all the authors before his death, except for the final drafting of the manuscript.)