Figure 1: The information Paradox.

by Scott Melville
figures by Shannon McArdel and Michael Gerhardt

You’ll never guess how Google autocompletes:

“Do black holes have…”

The answer:

“…no hair?

Fig1

This strange question has been debated by physicists for at least forty years, and today it seems we may be approaching an even stranger answer:

They have soft hair.

That is, at least, according to Stephen Hawking, who visited Harvard in April this year to give a sold-out lecture in Sanders Theatre. Professors Hawking and Malcolm Perry of Cambridge University have been working closely with Harvard’s own Professor Andy Strominger in order to explain some of the deepest mysteries surrounding black holes and the ultimate fate of information in the universe. This recent work of Hawking, Perry and Strominger has some profound implications for how we understand not only black holes, but all cosmological objects, and can be neatly summarized in the following theorem: “Black holes have soft hair.”

What are black holes?

Black holes are among the most extreme objects in our universe, places where gravitational effects get so strong that our current physical theories begin to break down. Once a theoretical construct, direct detection on September 14, 2015 (see our recent blog post about the LIGO discovery) finally proved their existence. Yet their very existence poses a profound challenge to our fundamental principles on how our world evolves. As we will see, if we want to predict the future of our universe, we need to understand how black holes work.

Gravitational forces can be thought of as currents in a river, pulling objects along in certain directions. In this river, a black hole is like a large, steep waterfall, where the current gets so incredibly strong that even light cannot escape. Much like how nothing flows back up from a waterfall, we know absolutely nothing about what lies inside a black hole, as nothing ever gets emitted.

Well, almost nothing. In 1974, Hawking showed that black holes can emit heat. As black holes slowly heat their surroundings, they give up energy (and therefore lose mass according to E=mc2) until there is nothing left. They evaporate, shrinking away until there is only empty space. This is a very slow process, analogous to the gradual erosion of the cliff underneath the waterfall. If you waited long enough, the cliff would eventually smooth into a gentle slope, and there would no longer be a frightening drop into the unknown.

What is black hole hair?

Almost every macroscopic object you know is incredibly complex. Take planets, for instance: no two planets are the same, because each has a vast number of properties. For the planets to be truly indistinguishable, they must have precisely the same density and composition at every point within, and this represents a truly colossal amount of information.

But black holes, on the other hand, are surprisingly simple. As far as an external observer is concerned, a black hole looks like a classical particle, completely characterized by just three numbers: its total mass, electrical charge, and spin (for example, the emitted heat is entirely determined by the mass). Different black holes with these same three properties are truly identical, meaning there are no measurements one could make on the outside to distinguish them. If ‘hair’ is the affectionate nickname given to features that help us tell objects apart, then black holes have next to none (hence ‘black holes have no hair’).

In order to understand the implications of this ‘no-hair theorem’ on how objects interact with a black hole, we need to address conservation laws in physics. A ‘charge,’ as defined by physicists, is some measurable quantity that doesn’t change with time. A familiar example is electrical charge, but mass and momentum can also be thought of as charges. Such quantities help physicists predict the future – if we start with one kilogram of ‘stuff’ in some configuration, we can confidently predict the total mass of the final configuration at a much later time (namely, one kilogram). You might recognize this as the principle of mass conservation. Black holes also obey these conservation laws: the charges for the final black hole must equal the sum of its original charges plus those carried by the objects it has swallowed. So, even though an object falling into a black hole is lost from our sight, conservation laws allow us to use measurements of the initial and final black hole to deduce a few properties the object had carried. Only a few, though, as the only measurable properties of the final black hole are its total mass, electrical charge, and spin. This has important consequences for how information is handled. You could toss in whole stars and planets of myriad shapes and colours, and the black hole would reduce all their complexity to only three numbers, meaning a lot of information has been lost.

Figure 1: The information Paradox.
Figure 1: The information paradox.

This represents a problem known historically as the information paradox. Suppose you set up some lab apparatus and carry out an experiment. You can use your scientific hypotheses to make a prediction. At the end of the experiment, you can jot down your findings, and use your results to support/refute your hypotheses. This is how science traditionally progresses: for example, if we initially mix hydrogen and oxygen, and then find that we are left with water, this supports our hypothesis that water is made up of hydrogen and oxygen. The implicit assumption is that the universe is deterministic, such that the final state of your experiment (your results) is completely determined by how you set it up initially. Conversely, if we understand the scientific principles governing a phenomenon and were to observe a certain outcome to an experiment, we should be able to deduce the initial configurations. It would be impossible to do science if the end of your experiment had absolutely nothing to do with how it started. Hence, the ability to make predictions using principles of causality is a founding principle of the scientific method.

A deterministic universe seems pretty close to our experience. But for a long time, black holes have presented a glaring counterexample to this principle. If a black hole gives off no information (besides the mass, electrical charge, and spin) about its history of consumption, and then completely evaporates into just empty space, then the final outcome would be totally independent of the initial state (which can contain stars, planets, etc.). This paradox strikes at the heart of determinism. If the future really is divorced from what happened in the past (what fell into the black hole when), then there’s no way to predict the future using knowledge of the present, hence threatening the core of science.

What makes hair ‘soft’?

Black holes (indeed, all masses) disturb the spacetime around them, causing distortion of clocks (time) and rulers (space). In theory, in order to measure traditional charges (hair) like the total mass, one simply arranges some clocks and rulers very close to the object and measures this local distortion. This disturbance fades as one gets further and further from the object, and so historically it was reasoned that detectors would be insensitive to the properties of distant objects. This belief is now being revised, in light of Strominger and his colleagues’ recent investigation of so-called ‘soft charges (hair)’, which correspond to non-trivial distortions in distant rulers and clocks that is sensitive to the consumption history of the black hole.

Figure 2: Black holes disturb the spacetime around them.
Figure 2: Black holes disturb the spacetime around them.

According to this new theory, if we were to set up two clocks a large distance from the black hole, then as it decays we will find a measurable change in the separation and delay between the clocks. The effect is very small, but may in the future be measurable by ground-based experiments like LIGO in the US, or its counterparts in Europe (Virgo, operational in 2016) or Japan (KAGRA, operational in 2018), or by satellite missions like the European Space Agency’s upcoming eLISA experiment (tentative launch date 2034). Therefore, although the black hole decays to just empty space, there is actually valuable information encoded in the structure of space and time itself–allowing us to reconstruct the properties of whatever the black hole swallowed before evaporating. This is known as the gravitational memory effect, distant rulers and clocks can remember something of the Universe’s history. In this case, the distant clocks are remembering the soft hair of the black hole.

If black holes do have such an effect on distant clocks–as Hawking, Perry and Strominger argue–then a huge step towards resolving the information paradox has been made. Black holes would have far more than just three numbers with which to record what they have swallowed up–every possible orientation of our distant rulers and clocks would measure a different soft hair, and so in principle there are an infinite number of such properties! This means that if one watched the late time erosion of the black hole carefully enough, one could reconstruct its entire history. Effectively, we would be remarrying the future with the past to guarantee that, given enough information about the present, we can predict the long term fate of our Universe.

What are the implications?

Though the theory of `soft-hair’ is still in its infancy – currently more a qualitative account than a rigorous mathematical description – it represents a promising resolution to the information paradox for black holes. Furthermore, there are myriad far-reaching implications.

All masses disturb the spacetime around them, and therefore should have measurable soft charges (in addition to their other conserved quantities like mass, momentum and electrical charge). This provides a whole new way of thinking about and probing the cosmological objects in our universe. By making precision measurements of changes in clocks/rulers here on Earth, we may be able to measure these soft charges of distant objects, allowing us to infer interesting things about their history (for example how neutron stars collide, or how the Universe as a whole has evolved).

Just as Newton taught us to predict how billiard balls collide using energy conservation, Hawking, Perry and Strominger are teaching us to predict how information flows between celestial bodies using soft charge conservation. Their insights help us to make sense of the vast cosmos around us, glimpse mankind’s future experiments, and pave the way towards a more complete description of our Universe.

Scott Melville is the 2015-16 von Clemm Fellow at Harvard University.

Original article:

Soft Hair on Black Holes
Hawking, Strominger, Perry
http://arxiv.org/abs/1601.00921

Further Reading:

Why the Black Hole Information Paradox is such a problem, Forbes
http://www.forbes.com/sites/ethansiegel/2015/09/05/why-the-black-hole-information-paradox-is-such-a-problem/#39b0fe455a7f

Stephen Hawking Hasn’t Solved the Black Hole Paradox Just Yet, Scientific American
http://www.scientificamerican.com/article/stephen-hawking-hasn-t-solved-the-black-hole-paradox-just-yet/

Hawking’s latest black-hole paper splits physicists, Nature
http://www.nature.com/news/hawking-s-latest-black-hole-paper-splits-physicists-1.19236

Media Coverage of Hawking’s Harvard Talk:

Could a black hole send you to another Universe? The Boston Globe
https://www.bostonglobe.com/metro/2016/04/18/black-holes-may-offer-way-out/ayFIhHEzAZyLjIZN7xWz4K/story.html

At Black Hole Talk, Stephen Hawking Draws Massive Audience, The Harvard Crimson
http://www.thecrimson.com/article/2016/4/19/stephen-hawking-black-hole-initiative/

Hawking at Harvard, Harvard Gazette
http://news.harvard.edu/gazette/story/2016/04/hawking-at-harvard/

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