12 Dec 2018
The story may now be repeating itself with white holes, which are essentially black holes in reverse. In another renowned textbook, the world-leading relativity theorist Bob Wald wrote that “there is no reason to believe that any region of the universe corresponds to” a white hole – and this is still the dominant opinion today. But several research groups around the world, including my group in Marseille, have recently begun to investigate the possibility that quantum mechanics could open a channel for these white holes to form. The sky might be teeming with white holes, too.
The reason to suspect white holes exist is that they could solve an open mystery: what goes on at the centre of a black hole. We see great amounts of matter spiralling around black holes and then falling in. All this falling matter crosses the surface of the hole, the “horizon” or point of no return, plummets towards the centre, and then? Nobody knows.
Einstein’s theory of general relativity, our current best description of gravity, predicts that in-falling matter ends up concentrating onto a single central point of infinite density, called a singularity. This is a sort of end to reality, a point where time itself stops and everything vanishes into nothingness. But this prediction is not reliable, because the centre of the hole is outside the domain of Einstein’s great theory. Here, gravity is so strong that quantum effects can no longer be neglected. To understand what happens, we need a quantum theory of gravity.
Quantum theory has a habit of solving problems of this kind. At the beginning of the 20th century, classical theory predicted that the energy of an electron orbiting the atomic nucleus would spiral down infinitely. Quantum theory clarified why this does not happen: it is forbidden by the discreteness of energy. The energy of the electron can change only by specific amounts, and it has a finite bottom level.
Quantum effects can similarly prevent infinite density from forming at the centre of a black hole. In this case, it is the discreteness of space-time itself, predicted by quantum theories of gravity such as loop quantum gravity (which I work on) that does the trick. There are no infinitely small points where density can become infinite. Space is composed of individual units, or quanta, which are small but finite. Falling matter can squeeze into a super-dense state, called a Planck star, but no more. And then? Then matter can do what matter commonly does at the end of a fall: bounce.
It cannot bounce up within the black hole, where things can only move downward. But here is the magic: quantum gravity allows the entire space-time geometry of the black hole to bounce – that is, to continue across the central point of the black hole into a separate and new region of space-time, where not just matter but also the entire space-time is bouncing out. This is what we call a white hole.
A ball that bounces up follows a trajectory that looks like a movie of its fall projected backwards. A white hole is like a movie of a black hole projected backward. From the outside, it is not much different: it has mass just like a black hole, so things are attracted by it and can orbit around it. But whereas a black hole is surrounded by a horizon through which it is possible to enter but not to exit, a white hole is surrounded by a horizon through which it is possible to exit but not to enter.
The theoretical possibility of white holes is predicted by general relativity. They are exact solutions of the equations of the theory. But they have long been viewed as mathematical niceties not representing anything real, precisely as were black holes in the past, because it was hard to see how they could originate.
As early as the 1930s, however, Irish physicist John Lighton Synge saw that a minimal adjustment in the solution of the equations of general relativity might allow the possibility that the geometry of the interior of a black hole could continue into a white hole. Quantum mechanics can permit such adjustment.
Where would the daughter white hole be located? Would it be far away, connected by a wormhole, or in a different universe? No, we don’t need outlandish speculations. It will be found at the same place where the black hole was, only in its future. Because of the peculiar elasticity of space-time as understood with Einstein’s theory, “the other side of the centre” can simply be in the future of the hole. This is hard to visualise, but the result is simple: in the first part of its life, the hole is black and matter falls in; but during the second, after the quantum transition, it is white and matter bounces out.
For this to happen, there should be a moment in which the horizon switches from being that of a black hole to being that of a white hole. Here again, it is quantum theory that allows this to happen, thanks to a well-known phenomenon known as quantum tunnelling. This is a brief violation of the standard, classical equations of physics that can happen, with low probability, even where one would not expect strong quantum phenomena. Tunnelling is what gives rise, for instance, to nuclear radioactivity. A particle trapped inside the atomic nucleus would not be able to escape according to classical mechanics, but quantum theory allows it to “tunnel below” the potential wall that traps it, and thus radiate outside the nucleus.
Tunnelling takes time. Radioactive substances remain quasi-stable for millennia. Similarly, black holes have long lifetimes. If we were to buy the classical theory, a black hole would be eternal. But nothing is eternal. Stephen Hawking showed that quantum theory implies that black holes slowly evaporate and shrink. As they shrink, the probability that they tunnel into a white hole increases. At some point, it happens. And again, the important thing is the geometry of space-time itself – this is the thing that is tunnelling. Instead of evolving according to the equations of classical general relativity, it suddenly tunnels from a black to a white hole horizon.
There is a puzzling aspect to this picture. We see black holes that are millions of years old, therefore a very long time is needed for a large black hole to tunnel into a white hole. But matter falling into the hole reaches the centre rapidly, in a matter of seconds. It would be equally quick to bounce out again. How can matter then find itself exiting a white hole so soon, when forming a white hole takes so long?
The answer is enchanting. Time is incredibly flexible in general relativity. We know it passes more slowly at sea level – closer to Earth’s centre – than on the mountains. Approaching a massive star or a black hole, it slows down even more. And this solves the puzzle: a very short time inside the hole can match a very long exterior time. Seen from the outside, the internal evolution of the hole appears like a bounce, but in super slow motion. The holes we see in the sky may simply be objects that collapse and bounce back out, perceived by us from the exterior in exaggerated slow motion.
A bonus from this scenario is that it solves the famous black hole information paradox – we expect information never to be completely lost in nature, but it is lost if time comes to an end inside a black hole. The solution is simple: if anything ends up bouncing out, information is recovered.
To be precise, the information paradox is a bit subtler than this. It stems from a widespread belief that the area of the horizon limits the number of possible different configurations of whatever is inside the hole. If too few configurations are available, the distinguishing features of the in-falling matter are lost, and so is information.
But I am convinced that this belief is wrong. It confuses the number of configurations distinguishable from the outside, which governs the external behaviour of the hole, with the much larger number of internal configurations, distinguishable from the inside, which increases even when the horizon shrinks. The inside of the black hole can be large even if its horizon is small – like a bottle can be large even if its neck is small – and can contain a very large amount of information, later released by the white hole.
All this gives an appealing scenario for the full life evolution of a black hole. In the interior of the hole there is no singularity, no place where space-time ends, and seen from the exterior a black hole is not eternal. Rather, at some time the black hole turns white and whatever fell inside it escapes.
The scenario is theoretically beautiful. Does it imply that the sky is truly full of white holes? And if so, can we see them?
The answer depends on things we do not yet fully understand. Most of the black holes we see in the sky are formed by the collapse of a star. These are too young and big to have already tunnelled into white holes – big holes live longer. But it is possible that smaller black holes formed in the fierce environment of the early universe, shortly after the big bang. These primordial black holes might have already tunnelled into white holes, or may be tunnelling today. But we are not sure about their number, and this makes predictions about current white holes uncertain.
A further source of uncertainty is the lifetime of a black hole. Detailed calculations have been attempted using loop quantum gravity, but they depend on approximations and are not yet conclusive. Still, we have a pretty firm bound between a maximum “long” lifetime, limited by Hawking’s evaporation time, and a minimum “short” lifetime required by the onset of quantum phenomena. This allows us to draw some preliminary conclusions.
If the lifetime is long, only small primordial holes have already turned white. This would mean most of the white holes currently in the sky should be of minimal size. The minimal white hole size is Planckian, namely around a microgram, or the weight of half an inch of a single strand of human hair.
This is an intriguing possibility because white holes of this size can be relatively stable, and they could be a component of the mysterious dark matter that astronomers have (indirectly) detected in the sky. Most other hypotheses on the nature of dark matter demand modifications of well-established laws of physics. For instance, they rely on theories predicting new entities called super-symmetric particles. But failures to detect such particles have raised questions about these theories.
The possibility that dark matter is instead composed of small black holes does not require anything more than established physics, namely general relativity and quantum theory, and is not ruled out by any observation. If this is correct, we have already observed white holes: they are the dark matter!
Alternatively, if the black hole lifetime is short, primordial black holes tunnelling today should have the mass of a small planet and could be exploding violently, transforming most of their mass into emitted radiation. This event should send us extremely energetic cosmic rays and short, violent signals in the microwave or radio band. The latter are particularly intriguing because similar signals have already been detected: the mysterious fast radio bursts recently observed by radio telescopes. Again, we might have already seen white holes.
We can’t confirm that these signals are indeed from white holes with just a few detections – other sources are possible. But there is a signature we will look for across a large sample: a flattened redshift. Signals emitted by distant and therefore younger white holes should produce shorter wavelengths than nearby, older ones. This is something we might be able to spot in high energy cosmic rays or fast radio bursts once we have enough data. If we do, we will have some evidence that white holes exist.
Finding evidence of white holes in the sky would be a beautiful step ahead in our understanding of the universe. They could represent the first direct observation of quantum gravity at work, and so open a window on the greatest problem in fundamental physics, the problem of understanding the quantum aspects of space-time.
I close by mentioning one last very speculative idea. Our universe might not have been born at the big bang: it may have bounced out from a previous collapsing phase. This possibility is allowed by loop quantum gravity and other theoretical frameworks. The quantum mechanism of the cosmic bounce is similar to the black-to-white-hole bounce. The Planckian white holes in today’s dark matter could have formed before the bounce. If so, the geometry of space-time at the bounce was not homogeneous as conventional cosmology suggests, but rather very crumpled, because each white hole is like a long spike out in the geometry of space-time.
This fact could be relevant for the mystery of the arrow of time – the question of why time goes in only one direction. The arrow of time might not be caused by the initial state of the universe being “special” (that is, low entropy), as is commonly believed. Instead, it may be a perspectival phenomenon related to the very “special” location of us observers: we are outside all the holes.
White holes are a plausible, albeit almost completely unexplored, possibility. We are yet to identify one, but then we didn’t recognise black holes for long time either.