Deep inside a black hole, the cosmos gets twisted beyond comprehension. Here, at some infinitesimal point of infinite density, the fabric of the universe gets so ludicrously warped that Albert Einstein’s general theory of relativity, which describes how mass bends space-time, ceases to make sense. At the singularity, our understanding falls apart.
As daunting as singularities are, each one is at least safely tucked away inside the event horizon of a black hole, the boundary beyond which we can’t see. This not only cloaks them from view, but also stops unknown effects they herald, namely the horrors of unpredictability, from leaching out into the wider universe. But what if singularities could exist outside black holes after all?
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That question, given fresh impetus in recent years by demonstrations that general relativity allows for this, has spurred theorists to probe singularities from a deeper perspective, folding in insights from the latest forays into the possible quantum foundations of gravity. Already, they are realising that this new approach “flips the script” on how we think about singularities, says at the Massachusetts Institute of Technology.
Fair warning: the work takes us into some labyrinthine physics. But by grappling with singularities in this way, Engelhardt and her colleagues are deciphering the enigmatic connections between the quantum realm and classical gravity – and reinforcing the revolutionary idea that the latter emerges from the former like a holographic projection. “There’s a lot that’s hanging in the balance,” says Engelhardt.
Soon after general relativity was published in 1915, physicists began finding solutions to its equations in which an incredibly dense ball of matter warps space-time so much that it plunges towards a point of infinite density and curvature. These are the singularities that have plagued the theory ever since.
The trouble with black holes
The trouble is that no one knows how to interpret what these infinities really mean in the physical universe. “Mathematically, we start losing control,” says Lisa Yang, also at MIT. In that sense, relativity, our best theory of gravity, appears to predict its own failure. The hope is that some new physics will come along and show us what we are missing, presumably involving quantum theory, which describes the behaviour of atoms and particles.
“‘What is the singularity?’ is a daunting question,” says at Harvard University’s Black Hole Initiative. “We don’t know what they are, we fundamentally don’t know how to describe them.”
No wonder many cosmologists initially hoped that singularities would turn out to be nothing more than a theoretical figment. Unfortunately for them, in 1965 the luminary cosmologist Roger Penrose proved that they are, in fact, an inescapable consequence of general relativity, occurring whenever matter collapses to form a black hole. “Singularities are ubiquitous,” says Engelhardt, an insight for which Penrose eventually won a share of the Nobel prize in physics.
In 1969, Penrose proposed that singularities are always concealed behind an event horizon, the outer edge of a black hole where gravity becomes so strong that nothing, not even light, can escape. This is known as the “weak cosmic censorship hypothesis” because it suggests that nature forbids visible or “naked” singularities. Physicists have good reason to think it must be true – not least that the existence of naked singularities would undermine the notion of a universe in which the laws of physics can predict what happens. “As long as you’re outside of the black hole, determinism is fine,” says , a black hole expert at Vanderbilt University in Nashville, Tennessee. “Whatever bad stuff is happening, is happening inside the horizon.”
Naked singularities were thus “brushed under the carpet”, says , a cosmologist at Ahmedabad University in India. Never properly dealt with, the concept lives on as a nagging reminder that an unproven hypothesis is the only thing preventing general relativity from losing its predictive power.
To make matters worse, in recent years theorists have demonstrated that naked singularities can indeed pop up as consequences of general relativity and related theories of gravity. For example, some researchers predict the existence of – similar in nature to black holes – that can stretch and pinch off, leaving behind a naked singularity. Others suggest that could also appear when black holes collide or by slowly emitting radiation. “The repertoire just keeps on getting larger and larger,” says Engelhardt.
Some of these naked singularities would only occur in hypothetical universes with more than three spatial dimensions, or in universes with a different kind of space-time curvature to ours. But these results still have implications for our cosmos, says Verheijden, and so they arguably signal the end of cosmic censorship as we know it. “It’s manifestly untrue,” she says. “Within classical general relativity, it can definitely be violated.”
And yet when we look at the night sky, we don’t see any naked singularities. “That black holes exist and [naked] singularities don’t, as far as we know, requires some kind of explanation,” says Engelhardt. “What is happening?”
To find out, in 2023, Engelhardt, Verheijden and Yang – along with MIT collaborators Åsmund Folkestad and Adam Levine – set about tackling the cosmic censorship hypothesis from an entirely new perspective. The results of their work, published in February, take the , says at the University of California, Santa Barbara. “It’s a significant advance,” he says.
Instead of searching for naked singularities in classical space-time theory, Engelhardt and her team investigated the nature of singularities and event horizons within the hypothetical framework of quantum gravity, which aims to unite general relativity and quantum mechanics – the two pillars of modern physics. “We set out to find a condition that would guarantee the formation of [event] horizons,” says Engelhardt.
Specifically, they used a popular quantum gravity approach called holography. The idea is that higher-dimensional space-time emerges from a lower-dimensional realm, described by quantum theory, in a way roughly akin to how a hologram is projected from a flat surface. You can translate between these two equivalent descriptions of reality using what you can imagine as a classical-quantum dictionary, known as the “AdS/CFT correspondence”, in which AdS is the “bulk” space-time and CFT is the quantum surface, or “boundary”.
Translating back and forth between the languages that describe the two realms, the researchers were looking to see if singularities in the bulk space-time have a signature in the boundary CFT, says Yang. They began by considering how black holes might appear in the boundary CFT.
Singularities and quantum gravity
It is conventional wisdom, at least among quantum gravity theorists, that black holes as they appear in the boundary CFT are “maximally chaotic”, says Engelhardt. This means the system is sensitive to its initial starting conditions, and small changes in these can lead to vastly different outcomes. Starting with this assumption, they found that a closely related concept called “psuedo-randomness” in the CFT correlates with the existence of an event horizon in bulk space-time. “You can use that as a diagnostic for the formation of a black hole,” says Lupsasca.
They called this new connection between pseudo-randomness and event horizons “cryptographic censorship” because it makes use of a growing toolkit from the fields of quantum information and cryptography to solve problems in fundamental physics. Among the strange consequences of these connections is the possibility that if you program a quantum computer with enough randomness then it may turn into a black hole itself (see “How to turn a quantum computer into a black hole”, left).
Using cryptographic censorship, the group then formulated a quantum version of cosmic censorship, which would go some way to explaining why we don’t see naked singularities. The researchers posit that the signature of space-time singularities in the CFT is this randomness. This means that any incoming matter or fields that hit a singularity would be reflected such that the singularity appears random – effectively scrambling its appearance. “We conjecture what we call Quantum Cosmic Censorship: that in quantum gravity, classical naked singularities should not exist,” says Verheijden.
Predictable space-time
To be clear, cryptographic censorship does permit the existence of very small naked singularities, in cases where there is insufficient randomness in the CFT to generate an event horizon, such as those left behind when black holes evaporate. They would just be too small to trouble determinism.
In any case, the work turns how we think about large naked singularities on its head, says Engelhardt. From the perspective of general relativity, naked singularities would be points where space-time and predictability break down. But in quantum gravity, large naked singularities would be in a “highly predictable space-time”, says Verheijden.
That is because the event horizon is a result of randomness. So, hypothetically, if you were to remove the event horizon – revealing the naked singularity – it would take the randomness with it. In other words, large naked singularities, were they to exist, wouldn’t be as riddled with randomness and unpredictably as we had assumed. “It’s a genuinely new perspective on this thing that’s unpredictable,” says Engelhardt.
For all that, the quantum version of cosmic censorship isn’t a watertight proof that naked singularities aren’t lurking in the cosmos. For one, the curvature of space-time described by AdS/CFT isn’t the same as that in our own universe. Quantum gravity theorists choose this as their sandbox to play in because it allows them to do otherwise intractable physics. “But it may or may not be related to how quantum gravity exactly works in our universe,” says Lupsasca. “That’s an open question.” When thinking about black holes and infinities, the details of space-time structure really matter, he says.
“They showed something that has the flavour of cosmic censorship,” says , also at MIT, who wasn’t involved with the work. “It’s more of a consequence of cosmic censorship, and if you can prove one of the consequences, then you can view it as evidence that [cosmic censorship] is true also,” he says.
Indeed, Engelhardt and her collaborators are more interested in taking the “spirit” of cosmic censorship and seeing what it would mean for quantum gravity itself. For one, the AdS/CFT correspondence assumes that black holes are the most common state in that universe. This allows theorists to understand black holes within quantum gravity as thermodynamic systems, whereby you can calculate their average properties, similar to how you measure the temperature or pressure of a box of gas molecules without knowing about the movements of individual particles.
Cryptographic censorship implies that, to all intents and purposes, a naked singularity is always cloaked by an event horizon, ensuring that black holes are far more common states than naked singularities. “If it weren’t true, our whole [AdS/CFT] house of cards would come crashing down,” says Harlow.
By digging into the foundations of AdS/CFT, the group also hopes to better grasp the convoluted way in which the holographic dictionary translates the quantum world into gravity. That is difficult because, instead of a one-to-one translation, each patch of the bulk universe seems to be encoded on the holographic plate, or CFT, more than once, in different places. In particular, figuring out which parts of the CFT describe the singularity and which parts describe the event horizon has frustrated progress. “A lot of AdS/CFT research has been hampered by the fact that things become very mysterious behind the event horizon, and our inability to separate the effects of the horizon from the effects of the singularity,” says Engelhardt.
For now, cosmic censorship remains unproven. But proving it was never really the point here. The real interest lies in what we can learn about the nature of black holes, and quantum gravity, by thinking deeply about this conjecture. And, even as it looks increasingly solid, some cosmologists, Lupsasca and Horowitz among them, are still hoping cosmic censorship isn’t true. “We would be delighted to see a naked singularity,” says Horowitz, “as we would actually have a way of getting observational evidence of quantum gravity.”
How to turn a quantum computer into a black hole
On the face of it, quantum computers, which leverage quantum physics to process information, have little to do with black holes. But in recent years, physicists have found hints of a deep connection between algorithms designed to make quantum computers more robust, known as error-correcting codes, and the fundamental structure of the universe.
It has to do with an approach to understanding the quantum origins of gravity known as holography, in which space-time is thought of as emerging from a flat surface, governed by quantum mechanics, as if it were a hologram. When researchers looked more closely at this model, their calculations suggested that this emergence seems to work much like a quantum error-correcting code.
Which raises a bonkers question: if you program the quantum description of a black hole into a quantum computer, would the equivalent space-time actually emerge in its vicinity – that is, would you create a real black hole in the process? "We haven't completely bitten the bullet on these implications," says Alex Lupsasca, a black hole expert at Vanderbilt University in Nashville, Tennessee. "Maybe you have to take that seriously."
Earlier this year, Netta Engelhardt and her collaborators at the Massachusetts Institute of Technology showed how a feature of quantum algorithms called pseudo-randomness, if there is enough of it, will always lead to the formation of a black hole event horizon (see main story). We don't yet have big enough quantum computers to program them with sufficient pseudo-randomness to create a black hole. But there is nothing to stop this being done in principle, says Engelhardt.
The idea that a quantum computer can create a black hole makes more sense when you consider that programming pseudo-randomness into a computer is akin to doing a very complex calculation, which requires a lot of information. "It's a lot of qubits. It's a lot of mass in a small amount of space," says Lisa Yang, one of Engelhardt's collaborators at MIT. "And so, by definition, it has to collapse into a black hole."
"Does that mean that you've created a black hole by doing this very complicated calculation? I think the answer is yes," says Lupsasca, who describes black holes as the "densest hard drives in the universe".
Of course, the moment a quantum computer collapses into a black hole, you can no longer access that computer. "Unless you're within the quantum computer," says Evita Verheijden at Harvard University's Black Hole Initiative. "But then you'd also be inside the black hole."
Thomas Lewton is a features editor at New Scientist
