Hawking and Ellis are in consensus with eternalism, saying that each solution to Einstein's equation encompasses the entire history of a universe - it is not just a picture of how things are, but a whole spacetime eventually materialized. (S. W. Hawking and Ellis 2008)
In Romero's argumentation, ontology is a class of entities accepted by a particular theory. Quine considers ontology as the domain of the variables related to a theory, thus the class of the theory of reference. And GR is not a spacetime theory, but the gravitational field and the interactions it determines. "Space-time is an ontological emergent property of the system formed by all existents, whatever they are. Because of the unique universality of gravity, models of space-time can be used to represent the gravitational field in General Relativity. More precisely, the affine connection of space-time represents the strength of the field, and the metric represents the gravitational potential. "(Romero 2013c)
Singularities in GR have triggered many philosophical problems, including their defining (as incomplete paths, missing points, or pathology of curvature) and their significance. If singularities have ontology, or they are limitations of our models, GR, respectively.
A black hole transforms the matter into a purely gravitational entity. Conversely, when it evaporates, space curvature is transformed into ordinary matter. (Curiel and Bokulich 2018) Thus, black holes are an important source for investigating the spacetime and ordinary matter ontology, and the conceptual problems underlying GR. Or if spacetime is dynamically abstract (Hilbert space) or more fundamentally, possibly an emerging entity belonging only to a physical theory.
Gustavo E. Romero (Romero 2013c) states that the existence of singular solutions in a background independence theory such as GR is a consequence of some contradictions at the level of the axiomatic basis of the theory. This contradiction appears from the approximation of the continuum adopted to model the gravitational field. A discreet theory should be developed, from which general relativity (and the usual notions of space and time) can appear as a kind of medium. This involves a major ontological change. Quantum gravity is considered by him to be a theory of relations between basic events and ontological emergence of spacetime and gravity. Quantum gravity would be such a fundamental theory that it could be considered an ontology rather than a physical one. The discreet nature of spacetime ontology can be formed by atomic events. The ontology of quantum gravity, and the world, in this perspective, would be a series of basic events.
In recent years, research has expanded from classical singularities of Penrose and Hawking's theories to the new paradigm of weak singularities, and Choptuik's theory of critical collapse. (Rendall 2005) Cosmological acceleration involves violations of the energetic state and requires a revision of singularity theories. Together with dark matter and energy, it assumes an expanding cosmological model that turns into a "big rip" singularity. (Starobinsky 1999)
The study of spatial-time singularities in the classical GR is still at the beginning. The black holes physics and the philosophy of cosmological singularities are still unexplored. In the face of singularities, science recognizes its limits. Here philosophy can be very helpful.