Uncovering the gauge symmetries of general relativity via Noether’s theorem.
By Merced Montesinos, Diego Gonzalez, and Mariano Celada
Symmetries are the cornerstone of modern physics. They are present in almost all its subfields and have become the language in which the underlying laws of the universe are expressed. Indeed, in the standard model of particle physics, our best understanding of nature down to the subatomic world, the interactions among fundamental particles are dictated by internal gauge symmetries.
Although the four fundamental interactions can be fitted within the framework of gauge theories, gravity still remains as the weird family member. While gravity can be conceived as a gauge theory on its own, it seems to be one that differs from those describing the non-gravitational interactions. Indeed, the latter are embedded within the so-called Yang-Mills theories, but gravity is something else.
Merced Montesinos (centre) is a theoretical physicist at Departamento de Física, Cinvestav, Mexico.
Diego Gonzalez (left) is a postdoctoral researcher at Instituto de Ciencias Nucleares, UNAM, Mexico.
Mariano Celada (right) is a postdoctoral researcher at Departamento de Física, UAM-I, Mexico.
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.
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.
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)
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.
I-Love-Q Probes of Modied Gravity
By Toral Gupta, Barun Majumder, Kent Yagi, and Nicolás Yunes
Although General Relativity has passed all tests carried out so far with flying colors, probes of the extreme gravity regime, where the gravitational interaction is simultaneously strong, non-linear and highly dynamical, have only recently began. This is timely because attempts to reconcile general relativity with quantum mechanics, be it in the form of string theory or loop quantum gravity, and attempts to explain cosmological observations, be it in the early or late universe, may require modifications to Einstein’s general theory. New electromagnetic telescopes, like the Neutron Star Interior Composition Explorer, and gravitational wave detectors, like advanced LIGO and Virgo, can now provide the first detailed observations of the extreme gravity regime. These new telescopes herald the era of extreme experimental relativity, allowing for new stringent constraints of deviations from Einstein’s theory, or perhaps, if we are lucky, pointing to signals of departures.
Toral Gupta is a graduate student at Indian Institute of Technology Gandhinagar.
Barun Majumder is a research assistant at Wilfrid Laurier University.
Kent Yagi is an assistant professor at University of Virginia.
Nicolás Yunes is an associate professor at Montana State University.
From quantum gravity to early universe cosmology using group field theory condensates
By Marco de Cesare, Daniele Oriti, Andreas Pithis, and Mairi Sakellariadou
“If you can look into the seeds of spacetime,
And say which grain will grow and which will not,
Speak then to me.”
– adapted quote from William Shakespeare’s, Macbeth
When we try to describe the earliest stages of the expansion of our Universe, the current picture of spacetime and its geometry as given by Einstein’s theory of General Relativity (GR) breaks down due to the extreme physical conditions faced at the Big Bang. More specifically, theorems by Hawking and Penrose imply that the cosmos emerged from a spacetime singularity. The existence of a cosmological singularity represents a main obstacle in obtaining a complete and consistent picture of cosmic evolution. However, there are reasons to believe that quantum gravitational effects taking place at the smallest scale could lead to a resolution of such singularities. This would have a huge impact for our understanding of gravity at a microscopic level, and for Cosmology of the very early Universe.
Marco de Cesare is a PhD student at King’s College London, working under the supervision of Mairi Sakellariadou on the cosmological consequences of quantum gravity.
Andreas Pithis is a PhD student at King’s College London, UK. He is a frequent visitor of the MPI for Gravitational Physics and held a visiting graduate fellowship at Perimeter Institute for Theoretical Physics, Canada.
Mairi Sakellariadou is a professor of theoretical physics at King’s College London and a member of the LIGO Scientific Collaboration. She is also Chair of the Gravitational Physics Division of the European Physical Society.
Daniele Oriti is a senior researcher and group leader at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam.
by Adriana V. Araujo, Diego F. López and José G. Pereira
The Quest for Consistency in Spacetime Kinematics
Newton’s inception of the theory for the gravitational interaction in 1687 was a landmark for modern physics. In addition to explaining all known gravitational phenomena of that time, Newton’s gravitational theory was consistent with the kinematic rules of the Galilei group, known as Galilei relativity. Such consistency provided an atmosphere of intellectual comfort, which lasted for more than two centuries.
From left to right, José, Adriana and Diego. Click here to see the authors taking advantage of all dimensions of a space section of the universe.
By the mid nineteenth century, most secrets of the electric and magnetic fields were already unveiled. Those advancements culminated with the publication by Maxwell of a comprehensive treatise on the unification of electricity and magnetism, which became known as Maxwell’s theory. This theory brought to the scene the first inconsistency of our tale. In fact, it became immediately clear that the electromagnetic theory was inconsistent with the Galilei relativity: electromagnetism was claiming for a new relativity. In response to this claim, and with contributions from Lorentz and Poincaré, Einstein published in 1905 the basics of what is know today as Einstein special relativity. According to this theory, for velocities near the velocity of light, spacetime kinematics would no longer be ruled by Galilei, but by the Poincaré group. Most importantly, electromagnetism was consistent with Einstein special relativity! Mission accomplished? Not quite! Continue reading
by J. Brian Pitts.
J. Brian Pitts is a Senior Research Associate, Faculty of Philosophy, University of Cambridge.
Observables and the Problem of Time
Mixing gravity and quantum mechanics is hard. Many approaches start with a classical theory and apply the magic of quantization, so it is important to have the classical theory sorted out well first. But the “problem of time” in Hamiltonian General Relativity looms: change seems missing in the canonical formulation.
Are Hamiltonian and Lagrangian forms of a theory equivalent? It’s not so obvious for Maxwell’s electromagnetism or Einstein’s GR, for which the Legendre transformation from the Lagrangian to the Hamiltonian doesn’t exist. It was necessary to reinvent the Hamiltonian formalism: constrained Hamiltonian dynamics. Rosenfeld’s 1930 work was forgotten until after Dirac and (independently) Bergmann’s Syracuse group had reinvented the subject by 1950. Recently a commentary and translation were published by Salisbury and Sundermeyer.
As canonical quantum gravity grew in the 1950s, it seemed less crucial for Continue reading
By Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou.
Black holes are perhaps the most fascinating predictions of General Relativity (GR). Yet, their very existence (conventionally) hinges on Special Relativity (SR), or more precisely on local Lorentz symmetry. This symmetry is the local manifestation of the causal structure of GR and it dictates that the speed of light is finite and the maximal speed attainable. Accepting also that light gravitates, one can then intuitively arrive at the conclusion that black holes should exist — as John Michell already did in 1783!
One can reverse the argument: does accepting that black holes exist, as astronomical observations and the recent gravitational wave direct detections strongly suggest, imply that Lorentz symmetry is an exact symmetry of nature? In other words, is this ground breaking prediction of GR the ultimate vindication of SR?
Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou from the School of Mathematical Sciences, University of Nottingham.
These questions might seem ill-posed if one sees GR simply as a generalisation of SR to non-inertial observers. On the same footing, one might consider questioning Lorentz symmetry as a step backwards altogether. Yet, there is an alternative perspective. GR taught us that our theories should be expressible in a covariant language and that there is a dynamical metric that is responsible for the gravitational interaction. Universality of free fall implies that Continue reading
Written by Jesper Møller Grimstrup, an independent danish theoretical physicist. He has collaborated with the mathematician Johannes Aastrup for more than a decade developing what they now call quantum holonomy theory. His present research is financed by an Indiegogo crowdfunding campaign (still open). Find more information on www.jespergrimstrup.org.
Could the laws of nature originate from a principle, that borders a triviality?
Does a final theory that cannot be explained by yet another, deeper theory, exist? What could such a theory possibly look like — and what might we learn from it?
Jesper Møller Grimstrup
These are the million dollar questions. Will the ladder of scientific explanations that take us from biology to chemistry and down through atomic, nuclear and particle physics, end somewhere? Will we one day reach a point where it is clear that it is no longer possible to dig deeper into the fabric of reality? Will we reach the bottom?
Together with the mathematician Johannes Aastrup I have developed a new approach to this question. Our theory — we call it quantum holonomy theory — is based on an elementary algebra, that essentially encodes how stuff is moved around in a three-dimensional space.
This algebra, which we call the quantum holonomy-diffeomorphism (QHD) algebra , is interesting for two reasons Continue reading
by Kirill Krasnov
Kirill Krasnov, Professor of Mathematical Physics, University of Nottingham. Pictured here visiting Newstead Abbey, Nottinghamshire
We seem to live in four space-time dimensions, and so should take the structures available in this number of dimensions seriously. One of these is chirality, see below for clarifications on my usage of this term. Related to chirality, there is a remarkable phenomenon occurring in General Relativity (GR) in four space-time dimensions. This phenomenon is so stunning that I would like to refer to it as the chiral miracle. It is well-known to experts. Still, even after almost 40 years after it had appeared in the literature, it has not become part of the background of all GR practitioners. I would like to use this CQG+ insight format to try to rectify this.
I start by reviewing the notion of chirality in four space-time dimensions. I then describe the “chiral miracle” that allows for chiral description(s) of gravity in Continue reading