The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, namely, to ensure that naked singularities would never emerge, since it predicts that whenever a singularity is formed an event horizon would always develop around it as well, to prevent the former from interacting directly with the rest of the Universe. Should this not be so, naked singularities could eventually form, in which case phenomena beyond our understanding and ability to predict could occur, since at the vicinity of the singularity both predictability and determinism break down even at the classical (e.g., nonquantum) level. More than 40 years after it was proposed, the validity of the hypothesis remains an open question. We reconsider CCH in both its weak and strong versions, concerning point-like singularities, with respect to the provisions of Heisenberg’s uncertainty principle. We argue that the shielding of the singularities from observers at infinity by an event horizon is also quantum mechanically favored, but ultimately it seems more appropriate to accept that singularities never actually form in the usual sense; thus no naked singularity danger exists in the first place.

Singularities, conceived as spacetime regions, where curvature (as described by scalar invariant quantities like

It should be noted here that CCH does not stem from some well-established physical law or mathematical theorem. Rather, it is a convenient hypothesis that, considering the catastrophic impact of the alternative, we gladly accept as (probably) true. Soon after it was proposed, it was declared as one of the most important open questions in classical general relativity [

Following this line of thinking we try here to engage quantum mechanics in the treatment of point-like singularities lying at a finite distance (as opposed to singularities lying at infinity or thunderbolts). The key idea proposed is to make appeal to Heisenberg’s uncertainty principle,

Point-like singularities are expected to form because of the unstoppable collapse of matter that occurs when a too large mass is concentrated in a too small volume. The volume of these singularities would effectively tend to zero by definition; thus they should occupy a single point of spacetime. In the case of a naked singularity, an observer at infinity (i.e., at sufficiently large distance away from it so as to be in an asymptotically flat region of spacetime) would in principle be able to determine its position with arbitrarily high accuracy by, for example, direct observation. When we make a measurement with uncertainty

What about s-CCH then? It is not hard to imagine a situation where a very large and massive system is in question (e.g., the central region of a galaxy); a trapped surface has already formed while observers living on a planet within the trapped region exist and expect quantum mechanics to hold at all times until they crash into the singularity that will develop some time in their future. Even though the soon-to-form singularity would remain unseen by observers at infinity (so w-CCH is satisfied), an observer inside the horizon would actually encounter a naked singularity (being at the same time at a significantly large distance away from it). All arguments presented in the paragraphs above hold true for this observer too, so a paradox a rises. The s-CCH is established to resolve the paradox by predicting that an observer would never actually see the singularity, but since it does not provide us with a mechanism capable of deterring this interaction, it looks more like the expression of a hope than a constraint imposed by some physical law. The only way out, then, is to admit that the notion of unstoppable collapse is wrong and, consequently, no point-like singularity is formed at all. Quantum effects should get so enhanced, at Planck scales, that they would manage to counterbalance the gravitational contracting forces to stop the collapse and prevent singularities from forming in the way we consider them to do today (e.g., the confinement of matter in an ever-decreasing volume, which means that it would acquire an ever-increasing momentum/energy, according, once again, to the uncertainty principle, so that it would end up behaving like a highly energetic gas whose pressure would constantly grow to counterbalance eventually the contraction, is a plausible mechanism to be explored in a work to come).

This approach, namely, the expectation that no singularity forms eventually, finds good support from a very interesting result by Geroch which crudely goes as follows: when a manifold admits a Cauchy surface (as is the case for the majority of physically reasonable spacetimes), then it also admits a global time function

To sum up, revisiting CCH on the grounds of the uncertainty principle, we arrive at the conclusion that w-CCH should hold true. However, since, by itself, it is insufficient to make the overall picture self-consistent, it is needed that s-CCH also applies. Yet the latter in its turn imposes so strict restrictions; that is, as a way out, one quite naturally arrives to admit that singularities never emerge in the usual sense, rendering CCH, in all its versions, unnecessary in the first place.