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FQXI ARTICLE
October 22, 2014

Heart of Darkness
An intrepid physicist attempts to climb into the core of black hole.
by Anil Ananthaswamy
FQXi Awardees: Veronika Hubeny
July 23, 2014
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Veronika Hubeny scales new heights in black hole research
Durham University
Imagine you are a pre-schooler listening to stories about dwarfs and giants. Would you have wondered whether giants perceive time differently than dwarfs? Veronika Hubeny did. That’s exactly the kind of question that consumed her as a kid. "I mused about whether dwarfs felt the day was longer than the giants," she says, chuckling now. But then it had been no laughing matter. "I never dared ask anyone this question, but I spent long hours really being bugged and bothered by it."

So, she was pondering something about the fundamental nature of time at five years of age? She laughs again, and says, "It’s of course a completely ill-defined question, and completely nonsensical, but I was very prone to getting intrigued by this sort of thing."

This might explain why Hubeny, who is now a physicist at Durham University in the UK, has spent her career asking fundamental questions about the nature of space and time. For example, where does the 4-dimensional fabric of spacetime—which Einstein told us pervades the universe—come from? Does it emerge from something more fundamental? No answers for such questions are forthcoming from his theory of gravity, general relativity, which is typically used to calculate how spacetime warps around massive bodies, like stars, but has little to say about what happens to it on the tiny scales inhabited by quantum particles. It is possible that when you zoom down even further to look at spacetime below this level, it breaks down. "We anticipate that classical spacetime, the continuous manifold of space and time, ceases to make sense at some small distances," says Hubeny.

Our notion of spacetime also disintegrates, according to general relativity, in the center of a black hole, known as a "singularity." What happens to an observer who falls into the black hole and encounters the singularity? "If you imagine a real life observer, that observer would die, but what happens to the stuff they are composed of?" says Hubeny. The answer could help physicists hunting for a theory of quantum gravity, which combines general relativity with the laws of quantum mechanics that dominate on small scales. "In general relativity, that stuff would end at the singularity, but in the full quantum gravity, something has to happen," Hubeny says.

I never had the feeling
growing up that there are
questions you don’t ask.
- Veronika Hubeny
Hubeny grew up near the Tatra Mountains in former Czechoslovakia, and developed an abiding love of mountains, along with her penchant for asking difficult questions. By elementary school she knew she wanted to be either a mountain guide or a physicist. Her choice was helped by the fact that she had an astrophysicist for a father. "I never had the feeling growing up that there are questions you don’t ask," she says.

Some real-life giants of physics have influenced her quest to answer such questions. Just when she started on her PhD at the University of California, Santa Barbara (UCSB), something seminal happened in field of string theory, the branch of physics that posits that elementary particles are composed of tiny loops of energy that vibrate in multiple dimensions. Physicist Juan Maldacena came up with a now eponymous conjecture tying together the mathematical descriptions of gravity and quantum field theory, using strings.

Maldecena pictured a special kind of space that exists in 5 dimensions (a maximally-symmetric negatively curved spacetime), which contains strings, black holes, and gravity. On the 4-dimensional surface of this space, live quantum particles—sans gravity—obeying the laws of quantum field theory. Maldacena’s striking claim was that the string theory describing what happens within this 5-dimensional space, is mathematically equivalent to a 4-dimensional quantum field theory describing what happens on the surface. "Such theories are referred to as holographic correspondences, because one side of the duality lives in fewer dimensions," says Hubeny. (See "The Cosmic Hologram.")

To answer questions about the emergence of spacetime and the fate of someone falling into a black hole, physicists like Hubeny want to solve the equations of the 5-dimensional string theory that describe the gravity-filled space within the volume. Unfortunately, however, they are quite intractable. Here’s where the duality comes in: You first recast the questions using the non-gravitational field theory of the surface, and solve them without having to deal with weird black-hole singularities. Then you translate the answer back to the 5-dimensional theory. Of course, it’s easier said than done. "The basic prerequisite is that we need to understand the dictionary," says Hubeny. "How do you translate from the string theory to the field theory side and vice-versa?"

Disentangling Spacetime

One way to translate between the two has become clear in recent years: There are hints, from work done by Leonard Susskind, Maldacena, and FQXi grant winner Mark Van Raamsdonk and others, that the geometry of spacetime within the 5-dimensional volume is related to quantum entanglement, on the 4-dimensional boundary surface, which links distant particles or regions so that their properties become permanently intertwined. (See "The Quantum Dictionary.") "You can sort of build spacetime by entangling the regions or you can decrease the amount of spacetime by disentangling,” says Hubeny.

In a similar vein, Hubeny, along with Mukund Rangamani, also at Durham, and Tadashi Takayanagi, at Kyoto University in Japan, have been investigating a boundary quantity called the "entanglement entropy"—a measure of the number of independent physical parameters in the field theory for that region. In particular, they have shown that this quantity is related to the area of an "extremal" surface in the bulk volume.


Beyond the Horizon
Could a mathematical trick help astrophysicists peer into the heart of a black hole?
Credit: NASA, and M. Weiss (Chandra X -ray Center)
It’s hard to visualize an extremal surface in 5 dimensions, but Hubeny has a cartoon description for a 3-dimensional volume. Imagine a ring on the boundary or surface, and a soap bubble inside the bulk, but one that is anchored on that ring. Mathematically speaking, an extremal surface is the soap bubble hanging within the bulk in a manner that minimises its surface area.

So, now, we have a boundary quantity, the entanglement entropy, that can be used to study the area of the extremal surface inside the bulk, which in turn is related to the geometry of the bulk. "Particularly interesting bits of geometry are where it starts breaking down," says Hubeny, such as in the interior of a black hole. While Hubeny had shown in 2012 that an extremal surface cannot penetrate a static black hole, she and her student Henry Maxfield conjectured that it just might penetrate a dynamically evolving black hole. The question was: can an extremal surface get to the black hole singularity? "If they penetrated arbitrarily close, we could hope to use entanglement entropy directly to study how the singularity gets resolved," says Hubeny.

However, their hopes were dashed. Their calculations showed that, unfortunately, extremal surfaces do not get close enough to the singularity (arXiv:1312.6887v3). "So, unsurprisingly, we as a community have to work harder to tease out the most interesting bits," says Hubeny.

We could hope to use
entanglement entropy
directly to study how
the singularity gets
resolved.
- Veronika Hubeny
And that’s exactly what Hubeny plans to do now. With her FQXi grant of $43,000, she hopes to further understand what kind of equivalences emerge between quantum information theory and spacetime geometry. Her efforts so far have not gone unnoticed. "Veronika is known for asking deep and fundamental questions from the space-time point of view,” says Don Marolf of UCSB.

Joe Polchinksi, also of UCSB, agrees. "Entanglement is the most mysterious part of quantum mechanics," he says. "Hubeny has contributed many important insights to this subject, especially concerning the black hole interior and its spacetime singularity."

Understanding the innards of a black hole and its spacetime singularity is quite a mountain to climb, but Hubeny is not deterred. She’s happy about her choice to pursue physics rather than become a mountain guide. "It was clear to me that my questions wouldn’t let me go," she says. Mountains, however, remain dear to her. "I like mountains even more than before."

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Perhaps this paper might help in your quest http://www.worldscientific.com/doi/abs/10.1142/S0219887814500595?queryID=%24%7BresultBean.queryID%7D

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