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).
● Alejandro Cárdenas-Avendaño is a graduate student at Montana State University and holds a junior researcher position at Fundación Universitaria Konrad Lorenz.
● Andrés F. Gutierrez is a graduate student at Universidad de Antioquia.
● Leonardo A. Pachón is an associate professor at Universidad de Antioquia.
● Nicolás Yunes is an associate professor at Montana State University, and co-founder of the eXtreme Gravity Institute.
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.
Aldo Riello ) is a senior postdoctoral fellow at Perimeter Institute.
Christophe Goeller is a PhD student at ENS Lyon and Perimeter Institute.
Etera Livine is a senior researcher at ENS Lyon.
Bianca Dittrich is a senior faculty at Perimeter Institute. Together they are the ABCE team, still looking for the right D to go deeper into holographic Duals.
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.
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.
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 . 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 . 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 , “Fast Self-forced Inspirals”, is a response to this challenge. Continue reading
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.
Kirill Krasnov, Professor of Mathematical Physics, University of Nottingham
Roberto Percacci, Associate Professor of Theoretical Particle Physics at SISSA, Italy
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 . 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.
Hal Haggard, Seth Asante, and Bianca Dittrich form a triangle area, the main variable in their new study of discrete gravity . 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
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?” , 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.
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.
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.
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
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!
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.
Dmitry Chernyavsky and Kamal Hajian Sevan lake in Armenia where we started to think about the cosmological conserved charge instead of cosmological constant.
Bypassing stability conditions and curing logarithmic singularities
By Jörg Frauendiener and Jörg Hennig
Assume you want to model a general relativistic spacetime. Due to the annoying limitations of conventional computers, like finite memory and processing speed, it is tempting to focus on a finite portion of the spacetime. Then, without waiting endlessly, one can obtain an approximate description of this portion. One just has to choose a suitable numerical method and solve the field equations for the metric at some set of grid-points. While this approach is standard, it introduces unpleasant problems. Firstly, the set of equations needs to be complemented with boundary conditions at the outer edges of this finite portion, in order to obtain a complete mathematical problem. This, however, is quite unphysical as usually no information about the actual behaviour at such an artificial boundary is available. Consequently, spurious gravitational radiation enters the numerical domain. Secondly, if one is interested in accurately describing gravitational waves, one should recall that these are only well-defined at infinity. Hence it is desirable to extend the simulation up to infinity.
Jörg Frauendiener and Jörg Hennig trapped at infinity.
Hopefully yes: Measure their Berry phases.
By Blagoje Oblak
Some years ago, at a dinner party, I met a fellow physicist who asked me what I was working on. I told him I was studying asymptotic symmetries — symmetries of space-time seen by observers located far away from all sources of the gravitational field. Remarkably, I said, these symmetries often have a beautiful infinite-dimensional structure and may provide new insights in our understanding of gravity. Somewhat sceptical, he replied: `Well surely this must be in some toy model — some extra dimensions, or postulated particles and fields… There’s no way this is directly relevant to our actual, real world!’ While I could understand his perspective, I also felt a little hurt by his cynicism towards theoretical science, so I was happy to retort: No, asymptotic symmetries do not require anything beyond what has been firmly established by experiment; just take pure general relativity, and their magic reveals itself.
- Blagoje Oblak performing a gravitational experiment in the Mediterranean. Photo credit: Geoffrey Mullier.