# Black hole behavior suggests Dr. Who's 'bigger on the inside' Tardis trick is theoretically possible

## Euclidean geometries don't really hold up within gravitational fields this strong.

Do black holes, like dying old soldiers, simply fade away? Do they pop like hyperdimensional balloons? Maybe they do, or maybe they pass through a cosmic rubicon, effectively reversing their natures and becoming inverse anomalies that cannot be entered through their event horizons but which continuously expel energy and matter back into the universe.

In his latest book, *White Holes**,* physicist and philosopher Carlo Rovelli focuses his attention and considerable expertise on the mysterious space phenomena, diving past the event horizon to explore their theoretical inner workings and and posit what might be at the bottom of those infinitesimally tiny, infinitely fascinating gravitational points. In this week's Hitting the Books excerpt, Rovelli discusses a scientific schism splitting the astrophysics community as to where all of the information — which, from our current understanding of the rules of our universe, cannot be destroyed — goes once it is trapped within an inescapable black hole.

*Excerpted from by *White Holes* by Carlo Rovelli. Published by Riverhead Books. Copyright © 2023 by Carlo Rovelli. All rights reserved.*

In 1974, Stephen Hawking made an unexpected theoretical discovery: black holes must emit heat. This, too, is a quantum tunnel effect, but a simpler one than the bounce of a Planck star: photons trapped inside the horizon escape thanks to the pass that quantum physics provides to everything. They “tunnel” beneath the horizon.

So black holes emit heat, like a stove, and Hawking computed their temperature. Radiated heat carries away energy. As it loses energy, the black hole gradually loses mass (mass is energy), becoming ever lighter and smaller. Its horizon shrinks. In the jargon we say that the black hole “evaporates.”

Heat emission is the most characteristic of the irreversible processes: the processes that occur in one time direction and cannot be reversed. A stove emits heat and warms a cold room. Have you ever seen the walls of a cold room emit heat and heat up a warm stove? When heat is produced, the process is irreversible. In fact, whenever the process is irreversible, heat is produced (or something analogous). Heat is the mark of irreversibility. Heat distinguishes past from future.

There is therefore at least one clearly irreversible aspect to the life of a black hole: the gradual shrinking of its horizon.

But, careful: the shrinking of the horizon does not mean that the interior of the black hole becomes smaller. The interior largely remains what it is, and the interior volume keeps growing. It is only the horizon that shrinks. This is a subtle point that confuses many. Hawking radiation is a phenomenon that regards mainly the horizon, not the deep interior of the hole. Therefore, a very old black hole turns out to have a peculiar geometry: an enormous interior (that continues to grow) and a minuscule (because it has evaporated) horizon that encloses it. An old black hole is like a glass bottle in the hands of a skillful Murano glassblower who succeeds in making the volume of the bottle increase as its neck becomes narrower.

At the moment of the leap from black to white, a black hole can therefore have an extremely small horizon and a vast interior. A tiny shell containing vast spaces, as in a fable.

In fables, we come across small huts that, when entered, turn out to contain hundreds of vast rooms. This seems impossible, the stuff of fairy tales. But it is not so. A vast space enclosed in a small sphere is concretely possible.

If this seems bizarre to us, it is only because we became habituated to the idea that the geometry of space is simple: it is the one we studied at school, the geometry of Euclid. But it is not so in the real world. The geometry of space is distorted by gravity. The distortion permits a gigantic volume to be enclosed within a tiny sphere. The gravity of a Planck star generates such a huge distortion.

An ant that has always lived on a large, flat plaza will be amazed when it discovers that through a small hole it has access to a large underground garage. Same for us with a black hole. What the amazement teaches is that we should not have blind confidence in habitual ideas: the world is stranger and more varied than we imagine.

The existence of large volumes within small horizons has also generated confusion in the world of science. The scientific community has split and is quarreling about the topic. In the rest of this section, I tell you about this dispute. It is more technical than the rest — skip it if you like — but it is a picture of a lively, ongoing scientific debate.

The disagreement concerns how much information you can cram into an entity with a large volume but a small surface. One part of the scientific community is convinced that a black hole with a small horizon can contain only a small amount of information. Another disagrees.

What does it mean to “contain information”?

More or less this: Are there more things in a box containing five large and heavy balls, or in a box that contains twenty small marbles? The answer depends on what you mean by “more things.” The five balls are bigger and weigh more, so the first box contains more matter, more substance, more energy, more stuff. In this sense there are “more things” in the box of balls.

But the number of marbles is greater than the number of balls. In this sense, there are “more things,” more details, in the box of marbles. If we wanted to send signals, by giving a single color to each marble or each ball, we could send more signals, more colors, more information, with the marbles, because there are more of them. More precisely: it takes more information to describe the marbles than it does to describe the balls, because there are more of them. In technical terms, the box of balls contains more *energy*, whereas the box of marbles contains more *information*.

An old black hole, considerably evaporated, has little energy, because the energy has been carried away via the Hawking radiation. Can it still contain much information, after much of its energy is gone? Here is the brawl.

Some of my colleagues convinced themselves that it is not possible to cram a lot of information beneath a small surface. That is, they became convinced that when most energy has gone and the horizon has become minuscule, only little information can remain inside.

Another part of the scientific community (to which I belong) is convinced of the contrary. The information in a black hole—even a greatly evaporated one—can still be large. Each side is convinced that the other has gone astray.

Disagreements of this kind are common in the history of science; one may say that they are the salt of the discipline. They can last long. Scientists split, quarrel, scream, wrangle, scuffle, jump at each other’s throats. Then, gradually, clarity emerges. Some end up being right, others end up being wrong.

At the end of the nineteenth century, for instance, the world of physics was divided into two fierce factions. One of these followed Mach in thinking that atoms were just convenient mathematical fictions; the other followed Boltzmann in believing that atoms exist for real. The arguments were ferocious. Ernst Mach was a towering figure, but it was Boltzmann who turned out to be right. Today, we even see atoms through a microscope.

I think that my colleagues who are convinced that a small horizon can contain only a small amount of information have made a serious mistake, even if at first sight their arguments seem convincing. Let’s look at these.

The first argument is that it is possible to compute how many elementary components (how many molecules, for example) form an object, starting from the relation between its energy and its temperature. We know the energy of a black hole (it is its mass) and its temperature (computed by Hawking), so we can do the math. The result indicates that the smaller the horizon, the fewer its elementary components.

The second argument is that there are explicit calculations that allow us to count these elementary components directly, using both of the most studied theories of quantum gravity—string theory and loop theory. The two archrival theories completed this computation within months of each other in 1996. For both, the number of elementary components becomes small when the horizon is small.

These seem like strong arguments. On the basis of these arguments, many physicists have accepted a “dogma” (they call it so themselves): the number of elementary components contained in a small surface is necessarily small. Within a small horizon there can only be little information. If the evidence for this “dogma” is so strong, where does the error lie?

It lies in the fact that both arguments refer only to the components of the black hole that can be detected from the outside, as long as the black hole remains what it is. And these are only the components residing on the horizon. Both arguments, in other words, ignore that there can be components in the large interior volume. These arguments are formulated from the perspective of someone who remains far from the black hole, does not see the inside, and assumes that the black hole will remain as it is forever. If the black hole stays this way forever—remember—those who are far from it will see only what is outside or what is right on the horizon. It is as if for them the interior does not exist. *For them*.

But the interior does exist! And not only for those (like us) who dare to enter, but also for those who simply have the patience to wait for the black horizon to become white, allowing what was trapped inside to come out. In other words, to imagine that the calculations of the number of components of a black hole given by string theory or loop theory are complete is to have failed to take on board Finkelstein’s 1958 article. The description of a black hole from the outside is incomplete.

The loop quantum gravity calculation is revealing: the number of components is precisely computed by counting the number of quanta of space on the horizon. But the string theory calculation, on close inspection, does the same: it assumes that the black hole is stationary, and is based on what is seen from afar. It neglects, by hypothesis, what is inside and what will be seen from afar after the hole has finished evaporating — when it is no longer stationary.

I think that certain of my colleagues err out of impatience they want everything resolved before the end of evaporation, where quantum gravity becomes inevitable) and because they forget to take into account what is beyond that which can be immediately seen — two mistakes we all frequently make in life.

Adherents to the dogma find themselves with a problem. They call it “the black hole information paradox.” They are convinced that inside an evaporated black hole there is no longer any information. Now, everything that falls into a black hole carries information. So a large amount of information can enter the hole. Information cannot vanish. Where does it go?

To solve the paradox, the devotees of the dogma imagine that information escapes the hole in mysterious and baroque ways, perhaps in the folds of the Hawking radiation, like Ulysses and his companions escaping from the cave of the cyclops by hiding beneath sheep. Or they speculate that the interior of a black hole is connected to the outside by hypothetical invisible canals . . . Basically, they are clutching at straws—looking, like all dogmatists in difficulty, for abstruse ways of saving the dogma.

But the information that enters the horizon does not escape by some arcane, magical means. It simply comes out after the horizon has been transformed from a black horizon into a white horizon.

In his final years, Stephen Hawking used to remark that there is no need to be afraid of the black holes of life: sooner or later, there will be a way out of them. There is — via the child white hole.