The following is an extract from our聽Lost in Space-Time聽newsletter. Each month, we dive into fascinating ideas from around the universe. You can聽sign up for聽Lost in Space-Time听丑别谤别.
Physics is littered with the remains of theories that once seemed destined to explain everything. A theory can dominate for decades, even centuries, only to be wiped out when new experimental results arrive or a fitter idea comes around. Before long, they鈥檙e relegated to little more than fossils in the scientific record.
Thermodynamics, though, is like the crocodile of physics 鈥� an unchanging ancient beast that has survived the field鈥檚 great mass-extinction events: the arrival of quantum mechanics, the fusion of space and time into one fabric, the discovery of the expanding universe. Thermodynamics has persisted through them all. Even Albert Einstein believed it would outlast quantum theory and general relativity, two fields he helped establish.
Advertisement
Now, it may finally have met its real test: an extremal black hole, a theoretical variety of cosmic behemoth that sits at the limits of the theory of general relativity. One of the basic laws of black hole thermodynamics suggests that nature could never make such a beast. But recent work has shown that nature may have found a loophole.
To see why that would be such a big deal, we need to return to the early 1970s, when our modern understanding of black holes was only beginning to take shape. Jacob Bekenstein, then a graduate student at Princeton University, pointed out that matter falling into a black hole seemed to disappear from the observable universe, taking its entropy with it.
Entropy tells us how many microscopic arrangements can produce the same observable state. Imagine a glass of water sitting on a table. To us, it has an obvious temperature, volume and pressure, but the molecules within can be arranged and moving in an immense number of different ways while the glass, overall, looks exactly the same. It鈥檚 worth mentioning that entropy is a very powerful tool 鈥� counting these arrangements can help us unpick what the microscopic components of a system are. According to the second law of thermodynamics, the total entropy of an isolated system always increases over time. So what happens when something falls into a black hole, crossing a threshold beyond which nothing can ever return? Is it just gone from the account of entropy in the cosmos? Certainly not without breaking the laws of physics. So, Bekenstein proposed a radical solution: black holes must possess entropy of their own.
Physicist Stephen Hawking initially objected. If a black hole had entropy, thermodynamics implied that it must also have a temperature 鈥� and anything with a temperature should radiate. That was awkward, given that the defining feature of a black hole was that nothing escaped it. But then physicists, including Hawking, crunched the numbers and saw that once they included quantum mechanics, black holes did emit a faint glow, now known as Hawking radiation. They had a temperature after all.
And when doing the maths, physicists noticed a striking resemblance between the laws that governed black holes and the laws of thermodynamics, which concern the transformation of work, entropy and energy in engines. In fact, there were rock-solid correspondences between the behaviour of black holes and the first two laws of thermodynamics, which state that energy cannot be created or destroyed and that entropy can never decrease in a closed system.
Physicists had little reason to think the third law would be any different. In ordinary thermodynamics, the third law says you can never cool a system all the way to absolute zero. The colder it gets, the harder it becomes to remove the last scraps of heat, until reaching zero would take an impossible amount of time or effort.
Black holes were thought to play by the same rule. A black hole is characterised by just three numbers: its mass, electric charge and spin. From those, you can work out the area of its event horizon, its temperature and its entropy. And, in line with the third law, it seemed that a black hole could never quite reach zero temperature, or stop emitting Hawking radiation altogether.
But in 2024, at the Massachusetts Institute of Technology and at the University of California, Berkeley, , as they鈥檙e known, could indeed exist. So, the third law of black hole physics may not be much of a law after all.
鈥淓xtremal black holes were thought of as an idealised, unattainable limit: something you could write down as a solution, but which could never be reached [through any real physical] process, but we proved that wrong,鈥� says Kehle.
The broken third law
We didn鈥檛 think this third law for black holes was true just because it mirrored thermodynamics. It also seemed to keep the rest of physics safe.
Charged and rotating black holes can have two horizons. The outer one is the familiar event horizon, the point beyond which nothing can return. Deeper inside lies the Cauchy horizon. Cross that and general relativity stops telling you what happens next: even perfect knowledge of the past would no longer be enough to predict the future.
Mathematical physicist Roger Penrose thought the Cauchy horizon would always stay safely inside the event horizon, keeping the singularity at the core of the black hole hidden from the rest of the universe. He called this idea cosmic censorship: a kind of built-in protection mechanism that stops us witnessing a place where the laws of physics have broken down 鈥� a so-called naked singularity.
But the black hole鈥檚 gravitational pull is counteracted by its charge and rotation. Increase either of these properties and the Cauchy horizon expands while the event horizon contracts. Eventually, the two coincide at a limit known as extremality. The gravitational intensity at the event horizon 鈥� a quantity known as its surface gravity 鈥� then falls to zero. Because a black hole鈥檚 Hawking temperature is proportional to this surface gravity, an extremal black hole has zero temperature and emits no thermal Hawking radiation.
Extremal black holes ride on the edge of this cosmic danger zone 鈥� right as the Cauchy horizon threatens to eclipse the event horizon and reveal a naked singularity 鈥� and were thought to be impossible. But Kehle and Unger found two ways around this.
Their models showed that an extremal black hole could form if you physically added charged matter to a black hole gradually, or fired a beam of charged particles into a region of empty space and caused it to collapse into an extremal black hole directly. Crucially, these mechanisms didn鈥檛 risk creating a naked singularity.
鈥淭he fact [that this work proves] extremal black holes can form dynamically tells us that these objects are not just mathematical limits. They can genuinely arise within classical gravity,鈥� says at the Free University of Brussels in Belgium.
What is extremality good for
That matters because these strange objects may provide a bridge between black holes in the messy, evolving universe and the highly idealised ones that have long appeared in string theory and quantum mechanics.
For decades, physicists have wanted to know what black holes are made of. Their entropy suggests that there must be many possible arrangements of microstates, corresponding to the same black hole. But what, exactly, is being rearranged?
That question is one reason theoretical physicists such as Toldo have been interested in extremal black holes for some time. Much of their appeal comes from their zero temperature, which would usually mean zero entropy. But despite having zero temperature, extremal black holes can still possess entropy. That makes them unusually clean models for exploring what a black hole鈥檚 microstates might actually be.
鈥淸String theory] gives you powerful techniques with which you can count the states inside a black hole,鈥� says Toldo. 鈥淵ou can try to start figuring out what the states inside the black hole are鈥� and what they鈥檙e made of. But until now, much of this work dealt with extremal black holes as idealised mathematical models. Showing that one can form dynamically brings those ideas a step closer to the kinds of objects that might genuinely arise in our universe.
There may even be a way to spot one. As matter tumbles towards a black hole, it can be squeezed and heated so violently that it gives off a burst of radiation. This is nothing like Hawking radiation: it comes from the infalling material itself. Around an ordinary black hole, the resulting disturbance soon dies away. But an extremal horizon lacks the usual damping effect, allowing part of it to linger and even grow. Last year, researchers should leave a distinctive fingerprint in the faint tail of radiation travelling out to distant observers.
But actually detecting an extremal black hole remains a distant prospect. For now, the more immediate implications are theoretical. If the third law of black hole physics can be broken, then the analogy between black holes and thermodynamic systems may not be as exact as we thought.
Kehle and Unger鈥檚 work has exposed more than a gap in our understanding of black holes. It raises the more unsettling possibility that we don鈥檛 fully understand thermodynamics either.
鈥淭his work made me realise that I understand black holes better than I understand classical thermodynamics,鈥� says Kehle. 鈥淔or example, when the third law says you can鈥檛 cool a system to absolute zero with a 鈥榝inite sequence of operations鈥�, what actually counts as an operation? There could be something more fundamental lurking there that we don鈥檛 know about.鈥�
鈥淲e鈥檝e disproved the third law as it was written, but we don鈥檛 yet understand this problem in any sense. There鈥檚 still a lot to be done,鈥� says Unger.
