Holography inside out: from 3D gravity to 2D statistical models

By Bianca Dittrich, Christophe Goeller, Etera R. Livine, and Aldo Riello


Despite many years of research, quantum gravity remains a challenge. One of the reasons is that the many tools developed for perturbative quantum field theory are, in general, not applicable to quantum gravity. On the other hand, non-perturbative approaches have a difficult time in finding and extracting computable observables. The foremost problem here is a lack of diffeomorphism-invariant observables.

The situation can be improved very much by considering space-time regions with boundaries. This is also physically motivated, since one would like to be able to describe the physics of a given bounded region in a quasi-local way, that is without requiring a detailed description of the rest of the space-time outside. The key point is that the boundary can be used as an anchor, allowing to define observables in relation to this boundary. Then we can consider different boundary conditions, which translates at the quantum level into a rich zoo of boundary wave-functions. These boundary states can correspond to semi-classical boundary geometries or superpositions of those. The states can also describe asymptotic flat boundaries, thus allowing us to compare with perturbative approaches. In this context, holography in quantum gravity aims to determine how much of the bulk geometry can be reconstructed from the data encoded in the boundary state.

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The boundary wave function Ψ are described by  dual theories defined on the boundary of the solid torus. These 2D boundary theories, obtained by integrating over all the bulk degrees of freedom of the geometry, encode the full 3D quantum gravity partition function.

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Fast Self-forced Inspirals

by Niels Warburton and Maarten van de Meent


LISA will fly. Since being given the green light by the European Space Agency a year ago, the scientific consortium around the Laser Interferometer Space Antenna (LISA) has been reorganising as it gears up to meet the challenge of building and operating a gravitational wave detector in space. This process has led to a renewed focus on the waveform templates that will be needed to extract the signals and estimate source parameters.

One of the key sources for LISA are extreme mass-ratio inspirals (EMRIs). In these binaries a stellar mass compact object (such as a black hole or neutron star) spirals into a massive black hole. Emitting hundreds of thousands of gravitational wave cycles in the millihertz band, LISA will detect individual EMRIs for months or even years. The low instantaneous signal-to-noise-ratio of the gravitational waves necessitates accurate waveform templates that can be used with matched filtering techniques to extract the signal from the detectors data stream. Coherently matching a signal over months or even years requires going beyond leading-order, flux-based black hole perturbation models and calculating the so-called ‘self-force’ that drives the inspiral [1]. Roughly, one can think of this self-force as arising from the smaller orbiting body interacting with its own perturbation to the metric of the massive black hole. To this end the recent “LISA Data Analysis Work Packages” document defined a number of source-modelling challenges that must be overcome before LISA flies [2]. One of these requires the community to:

Design and implement a framework for incorporating self-force-based numerical calculations, as they become available, into a flexible semi-analytical Kludge model that enables fast production of waveform templates

Our work [3], “Fast Self-forced Inspirals”, is a response to this challenge. Continue reading

Gravity and Unification

by Kirill Krasnov and Roberto Percacci


The geometric unification of gravity with the other interactions is not currently a popular subject. It is generally believed that a unified theory can only be constructed once a quantum theory of gravity is available. The purpose of this CQG+ contribution is to advocate that it may be fruitful and even necessary to reverse the logic: instead of “quantising in order to unify” it may be necessary to “unify in order to quantise”. If the latter perspective is correct, our current approaches to quantum gravity would be similar to trying to understand the quantum theory of electricity and magnetism separately before they were unified in Maxwell’s theory.

There are several arguments for such a change of priorities.

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Celebrating quantum gravity: the moon’s craters and conceptual revolutions

by Seth K. Asante, Bianca Dittrich, and Hal M. Haggard 


Fifty years ago this December the astronauts of the Apollo 8 mission were the first humans to ever see the far side of the moon. As they passed behind the moon they lost radio contact with mission control in Houston. They were completely isolated. Only recently have cockpit recordings of their reactions become public [1]. At first they couldn’t see the moon at all, but then the command module pilot James A. Lovell Jr. exclaims “Hey, I got the moon!”. William A. Anders, the lunar module pilot, asks excitedly “Is it below us?” and Lovell begins “Yes, and it’s—” when Anders interrupts him having spotted it. Deeply enthused the astronauts have dropped their technical patter and systems checks, which make up the main fabric of the recordings. Anders marvels “I have trouble telling the bumps from the holes.” In his excitement Anders completely loses his technical jargon. He can’t even recall the word ‘crater’. He is reacting to the moon. It is easy to feel his enthusiasm at this hidden wonder.

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Hal Haggard, Seth Asante, and Bianca Dittrich form a triangle area, the main variable in their new study of discrete gravity [5]. If you squint the image is even a bit like The Dark Side of the Moon’s cover art. The picture is taken in front of artwork by Elizabeth McIntosh hanging in the main atrium of the Perimeter Institute.

Quantum gravity is a deep puzzle of modern physics. Like the far side of the moon, much of the full theory is still hidden from view. But, it seems to me that we too seldom celebrate the great accomplishments that thinking about this puzzle has yielded. Two grand anniversaries both connected to gravity are to be celebrated this year. It’s a perfect moment to feel again the excitement that these discoveries represent and to connect to the enthusiasm and sense of exploration that quantum gravity can inspire. Continue reading

Low Energy? Think Positive!

Scott Melville, winner of the Best Student Talk Prize at BritGrav, which was sponsored by CQG, discusses the research that he’s doing on quantum gravity at Imperial College London.

Image courtesy of Steve Cross

Scott Melville, speaking at Bright Club on 28th April 2018. Image courtesy of Steve Cross

The present state of quantum gravity is rather unsatisfying. While perturbation theory works well at low energies, at high energies quantum gravity becomes incalculable, and leaves us hungry for answers. As we approach the Planck scale, perturbations become strongly coupled and we quickly lose perturbative control of our theory. A UV complete theory of gravity, which remains unitary and sensible to arbitrarily high energies, is hard to cook up.

We need new physics, to swallow these Planck-sized problems. This new physics shouldn’t be too heavy, or too light; not too strongly coupled, or too perturbative. We don’t yet know exactly what it should be, but it needs to hit a sweet spot. My research develops tools, called positivity bounds, which can help us better understand how low energy observables are connected to this unknown new physics.

One thing is for certain: quantum gravity is hard – and working on it sure builds up an appetite. When I’m not worrying about the fundamental nature of the Universe: I’m in the kitchen. While I may not be the best chef in the world, I make up for an abysmal lack of skill with a towering surplus of enthusiasm. You can flip anything in a pan, if you flip hard enough.

When it comes to deciding what to have for dinner, I take things very seriously: it can’t be too salty, or too sweet; not too spicy, or too bland.

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The Sound of Exotic Astrophysical “Instruments”

by Sebastian Völkel and Kostas Kokkotas


Could you distinguish the sound of a wormhole from an ultra compact star or black hole?

Such an exotic, though quite fundamental question, could be asked to any physicist after the groundbreaking and Nobel Prize winning discoveries of gravitational waves from merging black holes and neutron stars. Gravitational waves provide mankind with a novel sense, the ability to hear the universe. This analogy, between sound waves and gravitational waves, will bring to the minds of many physicists Mark Kac’s famous  question: “Can One hear the Shape of a Drum?” [1], and not just to the drummers amongst us. The possibility of this analogy is one of the ways in which gravitational waves are very distinct from the usual tool of astronomy, light.

To answer the question for our exotic instruments, we will rephrase it in a more technical form. In the simplest version one can describe linear perturbations of spherically symmetric and non-rotating models of wormholes and ultra compact stars. It is well known that the perturbation equations for these cases can simplify to the study of the one-dimensional wave equation with an effective potential. The solutions, which are usually given as a set of modes, represent the characteristic sound of the object. The so-called quasi-normal mode (QNM) spectrum is the starting point for our discussion.

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FIG. 1. Sebastian Völkel (right) is a PhD student in the Theoretical Astrophysics group of Professor Kostas Kokkotas at the University of Tübingen, located in the south of Germany. Among his research interests is the study of compact objects along with the associated gravitational wave emissions. More information about his research can be found here.
Professor Kostas Kokkotas (left) is leading the group of Theoretical Astrophysics at the University of Tübingen. The focus of his research is on the dynamics of compact objects (neutron stars & black-holes) as sources of gravitational waves in general relativity and in alternative theories of gravity. More information about the group can be found here.
Photo by Severin Frank.

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Undergraduate research and publications

by Nelson Christensen


The participation of undergraduates in scientific research is important for a number of reasons. First and foremost, undergraduates can make significant contributions to the science. In addition, research by undergraduates is now recognised to be an extremely important part of the educational process for these students. LIGO and Virgo have provided wonderful opportunities for undergraduates to experience the joys of physics  research. With guidance, students across the undergraduate physics spectrum can find a project suited to their level of expertise and their interests.

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Professor Nelson Christensen, who has conducted research and published with numerous undergraduates over the years.

Over the years at Carleton College I have had the thrill of seeing many students make real and significant contributions to LIGO and Virgo’s research efforts. When the students take their success from the classroom to research their joy for physics really springs out. But it should be noted that research is not a sure success for all undergraduate physics majors. I have seen “A” students who could never make the connection to the independent and original work required with a research project; that’s okay, research is not for everyone. On the other hand, I have worked with students who earned B’s and C’s in their physics classes, yet exploded with the opportunity of research; the applied nature of the physics motivated them, and consequently, often encouraged them to become better students in the classroom as well. Continue reading

COSMOLOGICAL CONS(tant → erved charge)

The road to black hole thermodynamics with Λ


by  Dmitry Chernyavsky and Kamal Hajian


What are volume and pressure in black hole thermodynamics? That is the question!

Chernyavsky Balloon

What do the gas in a balloon and a black hole have in common? For a regular CQG reader the answer should be obvious; both can be described within the framework of thermodynamics. However we know that the gas in balloon is characterised by volume and pressure, as well as other  thermodynamic quantities. So, a natural question arises about analogues of the volume and pressure for a black hole.
Answering this question, black hole physicists have noticed that if the universe is filled with a non-zero cosmological constant Λ, this mysterious entity can be absorbed in the energy-momentum tensor of matter, and its contribution resembles a perfect fluid with a pressure proportional to Λ. Continuing with this analogy, one can also introduce a ‘thermodynamic volume’ for a black hole. For instance, the appropriate volume which satisfies the first law of thermodynamics for the Schwarzschild black hole is equal to the volume of a ball with the same radius, but in flat space! Using the notions of the black hole pressure P and volume V, it is standard to vary the cosmological constant generalising the first law of black hole thermodynamics by V δP.

Chernyavsky authors

Dmitry Chernyavsky and Kamal Hajian Sevan lake in Armenia where we started to think about the cosmological conserved charge instead of cosmological constant.

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A good month for Einstein – gravitational starlight deflection during the Great American Eclipse

by Dr. Donald G. Bruns


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Don Bruns and his wife Carol on eclipse day at the Lions Camp on Casper Mtn. The tripod is bolted to the custom mosaic designed and built by his cousin Steve Lang.

After much anticipation, two experiments had great successes last year.  On August 17 2017, the LIGO/VIRGO collaboration monitored the merger of two neutron stars millions of light years away.  Only four days later in Wyoming, an experiment to measure the gravitational bending of starlight by the Sun acquired the best data since the idea was first tested in 1919, by Sir Arthur Eddington, in Africa.  I published my results on that experiment in Classical and Quantum Gravity on March 6, 2018.  My solo project to repeat Eddington’s achievement, which made Einstein famous, required a lot less manpower than LIGO!

Early last century, Einstein published his General Theory of Relativity that contained some unusual predictions, including the idea that massive bodies bend light beams.  The only way to test this would be during a total eclipse, when the sky would be dark enough to see stars close to the Sun, where the effect just might be measurable.

I started planning Eddington’s re-enactment when I found out that no one had attempted it since 1973 (also in Africa) and that no one had ever succeeded in getting all the parts to work during those precious few minutes of totality.  I assumed that with modern charge-coupled device (CCD) cameras and computerized telescopes, the experiment would be much easier.  I was wrong!  While some aspects were simplified (the Gaia star catalog provided accurate star positions, for example, and modern weather predictions and the compact equipment eased many logistics problems), dealing with pixels, turbulence, and a limited sensor dynamic range presented new challenges.

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Memories of Professor Stephen Hawking, 1942-2018

by Clifford Will, Editor-in-Chief, Classical and Quantum Gravity


The gravitational physics community, indeed the whole world, mourns the passing on Wednesday 14th March, 2018, of Stephen Hawking at the age of 76. The Editor, Board and staff of CQG offer their heartfelt condolences to Stephen’s family. There are already numerous extended obituaries of Stephen, and I won’t attempt one here (see for example the fine obituaries by Dennis Overbye in the New York Times and by Roger Penrose in the Guardian).

I will, however, offer two personal remembrances of Stephen that I hope will illustrate his humorous side. In 1972, I was a student at the famous Les Houches Summer School on black holes, where Stephen, Brandon Carter and Jim Bardeen lectured and wrote the seminal paper “The Four Laws of Black Hole Mechanics”, that suggested a formal analogy with the laws of thermodynamics. This was soon followed by papers by Jacob Bekenstein and by Stephen that made this more than an analogy. But one of the things I most remember about the school was the awe-struck look on my eight-year-old daughter Betsy’s face watching Stephen in his wheelchair demonstrating how he could wiggle his ears like Dumbo the elephant.

The second remembrance was a visit to Cambridge in 1978, where Stephen had asked me to give a colloquium on tests of GR and invited me and my wife to join him and Jane at “high table” dinner at his college, Gonville and Caius. I showed up in a psychedelic paisley shirt with ridiculously wide collars, baby blue flared jeans, and high-heeled boots (think John Travolta in “Saturday Night Fever”, but with hippie length hair). This was attire totally inappropriate for high table (hey, this was the 70s and was the best I had in my suitcase), but Stephen was delighted to have somebody there who made the stuffy and decorum-obsessed masters of the college more uncomfortable than he did. And when, during the ritual passing of the after-dinner liqueurs along the table, the college master chided me sternly for allowing the port to precede the claret, I thought Stephen was going slide out of his wheelchair, hysterical with laughter.

We have lost a remarkable scientist and a unique human being.


This work is licensed under a Creative Commons Attribution 3.0 Unported License.