What’s inside a black hole?

I have a multiple choice question for you.

What’s inside a black hole?

(A) An unlimited amount of stuff.
(B) Nothing at all.
(C) A huge but finite amount of stuff, which is also outside the black hole.
(D) None of the above.

The first three answers all seem absurd, boosting the credibility of (D). Yet … at the “Rapid Response Workshop” on black holes I attended last week at the KITP in Santa Barbara (and which continues this week), most participants were advocating some version of (A), (B), or (C), with varying degrees of conviction.

When physicists get together to talk about black holes, someone is bound to draw a cartoon like this one:

Penrose diagram depicting the causal structure of a black hole spacetime.

Part of a Penrose diagram depicting the causal structure of a black hole spacetime.

I’m sure I’ve drawn and contemplated some version of this diagram hundreds of times over the past 25 years in the privacy of my office, and many times in public discussions (including at least five times during the talk I gave at the KITP). This picture vividly captures the defining property of a black hole, found by solving Einstein’s classical field equations for gravitation: once you go inside there is no way out. Instead you are unavoidably drawn to the dreaded singularity, where known laws of physics break down (and the picture can no longer be trusted). If taken seriously, the picture says that whatever falls into a black hole is gone forever, at least from the perspective of observers who stay outside.

But for nearly 40 years now, we have known that black holes can shed their mass by emitting radiation, and presumably this process continues until the black hole disappears completely. If we choose to, we can maintain the black hole for as long as we please by feeding it new stuff at the same rate that radiation carries energy away. What I mean by option (A) is that  the radiation is completely featureless, carrying no information about what kind of stuff fell in. That means we can hide as much information as we please inside a black hole of a given mass.

On the other hand, the beautiful theory of black hole thermodynamics indicates that the entropy of a black hole is determined by its mass. For all other systems we know of besides black holes, the entropy of the system quantifies how much information we can hide in the system. If (A) is the right answer, then black holes would be fundamentally different in this respect, able to hide an unlimited amount of information even though their entropy is finite. Maybe that’s possible, but it would be rather disgusting, a reason to dislike answer (A).

There is another way to argue that (A) is not the right answer, based on what we call AdS/CFT duality. AdS just describes a consistent way to put a black hole in a “bottle,” so we can regard the black hole together with the radiation outside it as a closed system. Now, in gravitation it is crucial to focus on properties of spacetime that do not depend on the observer’s viewpoint; otherwise we can easily get very confused. The best way to be sure we have a solid way of describing things is to pay attention to what happens at the boundary of the spacetime, the walls of the bottle — that’s what CFT refers to. AdS/CFT provides us with tools for describing what happens when a black hole forms and evaporates, phrased entirely in terms of what happens on the walls of the bottle. If we can describe the physics perfectly by sticking to the walls of the bottle, always staying far away from the black hole, there doesn’t seem to be anyplace to hide an unlimited amount of stuff.

At the KITP, both Bill Unruh and Bob Wald argued forcefully for (A). They acknowledge the challenge of understanding the meaning of black hole entropy and of explaining why the AdS/CFT argument is wrong. But neither is willing to disavow the powerful message conveyed by that telling diagram of the black hole spacetime. As Bill said: “There is all that stuff that fell in and it crashed into the singularity and that’s it. Bye-bye.”

Adherents of (B) and (C) like to think about black hole physics from the perspective of an observer who stays outside the black hole. From that viewpoint, they say, the black hole behaves like any other system with a temperature and a finite entropy. Stuff falling in sticks to the black hole’s outer edge and gets rapidly mixed in with other stuff the black hole absorbed previously. For a black hole of a given mass, though, there is a limit to how much stuff it can hold. Eventually, what fell in comes out again, but in a form so highly scrambled as to be nearly unrecognizable.

Where the (B) and (C) camps differ concerns what happens to a brave observer who falls into a black hole. According to (C), an observer falling in crosses from the outside to the inside of a black hole peacefully, which poses a puzzle I discussed here. The puzzle arises because an uneventful crossing implies strong quantum entanglement between the region A just inside the black hole and region B just outside. On the other hand, as information leaks out of a black hole, region B should be strongly  entangled with the radiation system R emitted by the black hole long ago. Entanglement can’t be shared, so it does not make sense for B to be entangled with both A and R. What’s going on? Answer (C) resolves the puzzle by positing that A and R are not really different systems, but rather two ways to describe the same system, as I discussed here.That seems pretty crazy, because R could be far, far away from the black hole.

Answer (B) resolves the puzzle differently, by positing that region A does not actually exist, because the black hole has no interior. An observer who attempts to fall in gets a very rude surprise, striking a seething “firewall” at the last moment before passing to the inside. That seems pretty crazy, because no firewall is predicted by Einstein’s trusty equations, which are normally very successful at describing spacetime geometry.

At the workshop, Don Marolf and Raphael Bousso gave some new arguments supporting (B). Both acknowledge that we still lack a concrete picture of how firewalls are created as black holes form, but Bousso insisted that “It is time to constrain and construct the dynamics of firewalls.” Joe Polchinski emphasized that, while AdS/CFT provides a very satisfactory description of physics outside a black hole, it has not yet been able to tell us enough about the black hole interior to settle whether there are firewalls or not, at least for generic black holes formed from collapsing matter.

Lenny Susskind, Juan Maldacena, Ted Jacobson, and I all offered different perspectives on how (C) could turn out to be the right answer. We all told different stories, but perhaps each of us had at least part of the right answer. I’m not at KITP this week, but there have been further talks supporting (C) by Raju, Nomura, and the Verlindes.

I had a fun week at the KITP. If you watch the videos of the talks, you might get an occasional glimpse of me typing furiously on my laptop. It looks like I’m doing my email, but actually that’s how I take notes, which helps me to pay attention. Every once in a while I was inspired to tweet.

I have felt for a while that ideas from quantum information can help us to grasp the mysteries of quantum gravity, so I appreciated that quantum information concepts came up in many of the talks. Susskind invoked quantum error-correcting codes in discussing how sensitively the state of the Hawking radiation depends on the information it encodes, and Maldacena used tensor networks to explain how to build spacetime geometry from quantum entanglement. Scott Aaronson proposed the appropriate acronym HARD for HAwking Radiation Decoding, and argued (following Harlow and Hayden) that this task is as hard as inverting an injective one-way function, something we don’t expect quantum computers to be able to do.

In the organizational session that launched the meeting, Polchinski remarked regarding firewalls that “Nobody has the slightest idea what is going on,” and Gary Horowitz commented that “I’m still getting over the shock over how little we’ve learned in the past 30 years.” I guess that’s fair. Understanding what’s inside black holes has turned out to be remarkably subtle, making the problem more and more tantalizing. Maybe the current state of confusion regarding black hole information means that we’re on the verge of important discoveries about quantum gravity, or maybe not. In any case, invigorating discussions like what I heard last week are bound to facilitate progress.