Understanding exact space-times

By Jiří Podolský 


General relativity is a unique gem, Einstein’s most brilliant idea, and his greatest gift to humankind. Conceived in 1915, it still remains the best theory of gravity. I’m sure Einstein himself would be surprised how remarkably well it describes reality, even in the most violent and dynamical situations. Just recall its recent spectacular vindication by the first direct detection of gravitational waves from binary black hole mergers at cosmological distances. What an achievement! Gravitational waves, black holes, cosmology – all three main ingredients and predictions of Einstein’s theory combined together.

Exact space-times

As we all know, Einstein’s equations determine the space-time geometry, which is the gravitational field. And we must take all their predictions seriously. Exact solutions to Einstein’s field equations include the mathematical truth about the physical reality. Unfortunately, it is often obscured, usually very deeply hidden. To dig out the physically measurable invariant quantities and consequences, is a painful mining process involving various techniques and methods. It is the real art of science.

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It is essential to be well-equipped for the investigation of exact space-times. Nevertheless, here we are preparing to descend old silver mines in Kutná Hora, the source of great wealth of the Kingdom of Bohemia in the Middle Ages. (Jerry Griffiths and Jiří Podolský, April 2006)

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Putting a limit on the mass of the graviton

by Clifford Will


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Clifford Will (http://www.phys.ufl.edu/~cmw/) is Distinguished Professor of Physics at the University of Florida and Chercheur Associé at the Institut d’Astrophysique de Paris. Until the end of 2018, he is Editor-in-Chief of CQG.

According to general relativity, the gravitational interaction is propagated as if the field were massless, just as in electrodynamics.   Thus the speed of gravitational waves is precisely the same as the speed of light, a fact spectacularly confirmed when gravitational waves and gamma rays from the binary neutron star merger event GW170817 arrived within 1.74 seconds of each other, even after traveling for 120 million years.

But some modified gravity theories propose that the field could be massive, so that gravitational waves might propagate more slowly than light, and with a speed that depends on wavelength.   The shorthand term for this is a “massive graviton”, although quantum gravity plays no role in this discussion.  This is entirely a classical phenomenon.

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If space-time has defects, how could we find out?

By Sabine Hossenfelder


Whether space and time come in discrete chunks is one of the central questions of quantum gravity, the still missing unification of quantum theory with gravity. Discretization is a powerful method to tame infinities exactly like the ones that appear when we try to quantize gravity. It is thus not surprising that many approaches to quantum gravity rely on some discrete structure, may that be condensed matter analogies, triangulations, or approaches based on networks.

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Sabine Hossenfelder

Many researchers in the field hope that besides taming the infinities that appear in the quantization of gravity, discretization will also prevent the formation of singularities that general relativity predicts, for example at the big bang and inside black holes.  If space-time was fundamentally made of finite-sized chunks, then the singularities would merely be mathematical artefacts, just like singularities in hydrodynamics are merely mathematical artefacts of using the fluid-approximation on distances when we should instead use atomic physics. Continue reading

Finding order in a sea of chaos

By Alejandro Cárdenas-Avendaño, Andrés F. Gutiérrez, Leonardo A. Pachón, and Nicolás Yunes


Hunting for constants of the motion in dynamical systems is hard. How can one find a combination of dynamical variables that remains unchanged during a complicated evolution? While it is true that answering this question is not trivial, symmetries can sometimes come to the rescue. The motion of test particles around a spinning (Kerr) black hole, for example, has a conserved mass, energy and angular momentum. Nevertheless, simple symmetries can only go so far. Given the complexity of the radial and polar sector of Kerr geodesics, it came as a complete surprise when Carter found, in 1968, a fourth constant of the motion, which was later found to be associated with the existence of a Killing tensor by Walker and Penrose. This fourth constant then allowed the complete separability of the geodesic equations, thus proving the integrability of the system, and as a consequence, that the motion of a test particle around a Kerr black hole is not chaotic in General Relativity (GR).

 

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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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