A Note on Genericity and Stability of Black Holes and Naked Singularities in Dust Collapse

TL;DR

This paper reexamines the concepts of genericity and stability in dust collapse models, arguing that the definition of genericity impacts whether black holes or naked singularities are considered typical outcomes.

Contribution

It clarifies the notion of genericity in gravitational collapse, proposing a physically meaningful measure that alters the perceived likelihood of naked singularities.

Findings

Reconsideration of genericity definitions in gravitational collapse

Proposed measure shows naked singularities are not necessarily non-generic

Implication that black holes and naked singularities may both be physically plausible outcomes

Abstract

We comment here on the results in Ref [4] that showed naked singularities in dynamical gravitational collapse of inhomogeneous dust to be stable but non-generic. The definition of genericity used there is reconsidered. We point out that genericity in terms of an open set, with a positive measure defined suitably on the space of initial data, is physically more appropriate compared to the dynamical systems theory definition used in [4] which makes both black holes and naked singularities non-generic as collapse outcomes.