Boundaries, Corners and Creases

 by Joseph Samuel.

Cricketing nations have a very good idea what a boundary is, it’s good for a cool four runs, without the bother of running! Corners are tense moments in a football (soccer to some) match when a well struck ball can curve into the goal. The crease is what a batsman lunges for when the wicket keeper ….. wait! this is not a sports column, but CQG+! Let’s back up and explain what our paper really is about.

In a path integral approach to quantum gravity, one has to divide up spacetime into pieces and focus on the action within each piece. In the elementary case of particle mechanics, this “skeletonisation” converts the action expressed as a Riemann integral into a discrete sum. A desirable property of the action is that it should be additive when we glue the pieces back together. This is achieved only when one properly takes into account the boundaries of the pieces.  The boundaries can be spacelike, timelike or null. Much work has focused on the first two cases. The Einstein–Hilbert Action principle for spacetime regions with null boundaries has only recently attracted attention (look up the Arxiv for papers by E. Poisson et al and Parattu et al; references would not be consistent with the chatty, informal style of  CQG+). These papers deal with the appropriate boundary terms that appear in all boundary signatures.

Our paper (authors: Ian Jubb, Joseph Samuel, Rafael Sorkin and Sumati Surya) gives a unified approach to all boundary signatures using Cartan’s tetrad formalism. An unexpected feature of the boundary term required here is that it is not gauge invariant under local Lorentz transformations (although its variation is). As the tetrad formalism may not be familiar to some readers of CQG, we also give a treatment in terms of metrics. When the boundary has corners the action has to also contain corner terms. Cartan’s tetrad formalism gives a simple way to arrive at the corner terms, exploiting the gauge non invariance of the boundary terms.

Spacetime boundaries can be null. A classic example is the region exterior to a black hole, whose boundary is a frozen wavefront, the event horizon. Horizons can have creases where the null normal is discontinuous, as happens when new null generators enter (or leave) the horizon. Another example of a null boundary is that which appears in a Causal diamond. A causal diamond is the intersection of a past set with a future set and looks (when it is drawn on a blackboard) much like the diamond in a baseball game. Yet another example of a null boundary is Scri, asymptotic null infinity. Null boundaries deserve special attention since their normals are also their tangents. Our unified treatment paints all kinds of boundaries with the same brush.

A photograph taken on the terrace of the library building during the workshop around December 2015.

This work, involving a collaboration across continents had its genesis in a series of workshops organised at the Raman Research Institute in the last few years by Sumati Surya. Come December, when the skies are grey in the northern latitudes, some of our colleagues, like migrating birds, wing their way south, to the Raman Research Institue (RRI) in Bangalore, India. The photo above shows some of them with friends and families. Visible in the photograph are the four authors of our paper. The photograph is taken on the terrace of the library building, where the talks took place. The talks and discussions revolve around general relativity (mostly from the Causet point of view championed by Sorkin), Quantum Measure theory, entanglement entropy, the cosmological constant and topology change. Sometime in December 2014, the discussions around the meeting raised the question of null boundaries. This question was partly answered and then revived at the subsequent meetings and culminated in the paper. Do take a look at it.

A few words about the RRI campus may be in order here: it is wooded and distinctly cooler than the surrounding areas because of the foliage. The trees are home to a variety of bird, animal and insect life. Common birds are sunbirds, bulbuls, koels and barbets, whose calls you can listen to as a welcome distraction from work. There is a dwindling population of slender lorises and a thriving population of lazy cats. During November / December / January the skies are clear blue (though dotted with soaring kites) and the wooded campus attracts a seasonal feathered visitor, the paradise flycatcher. Each year these birds stop at the Institute campus for about two weeks before going further south to their destination in the Nilgiri hills. What attracts the birds here is probably the insect life, which is also pretty diverse (Arachnophobes are advised to desist from clicking on this link.).

The Raman Institute has groups doing research in four select areas of physics: Astrophysics, Theoretical Physics, Soft Condensed Matter and Light and Matter Physics. There is also research in chemistry and a substantial thrust in instrumentation related to Astronomical Observations at telescopes in India and around the world. For more information on this look at Facebook or Twitter. The theoretical physics group has interest mainly in General Relativity and Non equilibrium Statistical Physics. Apart from the permanent faculty at RRI, we have postdocs, PhD students and a vibrant Visiting Student program at the Bachelor’s and Master’s level. We also have an outreach programme to interface with schools and colleges. Check out our homepage for more details.

About the Author: I am a theoretical physicist at the Raman Research Institute. My interests include general relativity, optics, the geometric phase in quantum mechanics, DNA elasticity and science popularisation. I keep moderately fit by raising and lowering indices. I enjoy gardening and relax by cooking exquisitely textured lacy appams for my friends.

Read the full article in Classical and Quantum Gravity:
Boundary and corner terms in the action for general relativity
Ian Jubb et al 2017 Class. Quantum Grav. 34 065006

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Is the Cosmic Microwave Background Gaussian?

by Thomas Buchert, Martin J. France & Frank Steiner.

Thomas Buchert is Professor of Cosmology at the University of Lyon 1, working at the ‘Centre de Recherche Astrophysique de Lyon’ (CRAL)

This challenging question touches on the initial conditions of the primordial Universe, on modeling  assumptions, and statistical ensembles generating the Cosmic Microwave Background.

Our CQG paper explores model-independent approaches to these challenges.

We observe only a single Universe, the one we live in. We cannot rerun cosmic history to see how actual observations might have varied. Nor can we communicate with distant aliens to build an ensemble of observations of the Universe from different vantages in space and time. The only possibility that remains is to make a model of the Universe. Running this model a large number of times, we can generate an ensemble of realizations of the Cosmic Microwave Background (CMB) sky maps. In principle, it is then possible to answer the question, whether there is a single realization of the chosen model that agrees with what is observed. Moreover, we should determine the probability of finding this single realization within the ensemble of patterns that our model allows. To do this we have to Continue reading

Things Change – Even in Hamiltonian General Relativity!

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

Advancing the Search for Gravitational Waves with Next-Generation Citizen Science

by Michael Zevin.


Michael Zevin is a third-year doctoral student in astrophysics at Northwestern University. He is a member of the LIGO Scientific Collaboration, and in addition to citizen science and LIGO detector characterization his research focuses on utilizing gravitational-wave detections to learn about binary stellar evolution and the environments in which compact binaries form.

With the first observations of gravitational waves and the discovery of binary black hole systems, LIGO has unveiled a new domain of the universe to explore. Though the recent signals persisted in LIGO’s sensitive band for a second or less, these last words of the binary that were spewed into the cosmos provided an unprecedented test of general relativity and insight into the progenitor stars that subsequently formed into the colliding black holes. However, the hunt is far from over. With LIGO’s second observing run underway, we can look forward to many more gravitational-wave signals, and as is true with any new mechanism for studying the cosmos, we can also expect to find the unexpected.

The extreme sensitivity required to make such detections was acquired through decades of developing methods and machinery to isolate the sensitive components of LIGO from non-gravitational-wave disturbances. Nonetheless, as a noise-dominated experiment, LIGO is still susceptible to Continue reading

Tails from Eccentric Encounters

by Nicholas Loutrel.


Nicholas Loutrel is a Graduate Student in the eXtreme Gravity Institute at Montana State University.

A new method of computation aims to fill in the gaps in our knowledge of gravitational waves from eccentric binaries.

The modeling of gravitational waves (GWs) suitable for detection with ground-based detectors has been mostly focused on binary systems composed of compact objects, such as neutron stars (NSs) and black holes (BHs). Binaries that form with wide orbital separations are expected to have very small orbital eccentricity, typically less than 0.1, by the time their GW emission enters the detection band of these instruments. However, in dense stellar environments, unbound encounters between multiple compact objects can result in the formation of binaries with high orbital eccentricity (close to, but still less than unity) and whose GW emission is in band for ground-based detectors. Such systems are expected to be Continue reading

Issue of the Beginning: Initial Conditions for Cosmological Perturbations

by Abhay Ashtekar and Brajesh Gupt.


Abhay Ashtekar holds the Eberly Chair in Physics and the Director of the Institute for Gravitation and the Cosmos at the Pennsylvania State University. Currently, he is a Visiting Professor at the CNRS Centre de Physique Théorique at Aix-Marseille Université.

Although our universe has an interesting and intricate large-scale structure now, observations show that it was extraordinarily simple at the surface of last scattering. From a theoretical perspective, this simplicity is surprising. Is there a principle to weed out the plethora of initial conditions which would have led to a much more complicated behavior also at early times?

In the late 1970s Penrose proposed such a principle through his Weyl curvature hypothesis (WCH) [1,2]: in spite of the strong curvature singularity, Big Bang is very special in that the Weyl curvature vanishes there. This hypothesis is attractive especially because it is purely geometric and completely general; it is not tied to a specific early universe scenario such as inflation.

However, the WCH is tied to general relativity and its Big Bang where classical physics comes to an abrupt halt. It is generally believed that quantum gravity effects would intervene and resolve the big bang singularity. The question then is Continue reading

Quantum mechanics meets CMB physics

by Massimo Giovannini.


Since 1991 Massimo Giovannini has extensively researched, taught and written on high-energy physics, gravitation and cosmology. He wrote over 180 papers and various review articles. He is the author of a book entitled “A primer on the physics of Cosmic Microwave Background” published in 2008.

Which is the origin of the temperature and polarization anisotropies of the Cosmic Microwave Background? Classical or quantum? The temperature and the polarization anisotropies of the Cosmic Microwave Background (CMB) are customarily explained in terms of large-scale curvature inhomogeneities. Are curvature perturbations originally classical or are they inherently quantum mechanical, as speculated many years ago by Sakharov?

In the conventional view these questions are quickly dismissed since the quantum origin of large-scale curvature fluctuations is, according to some, an indisputable fact of nature. This is true if and when Continue reading

Want to crush a singularity? First make it strong and then …

by Parampreet Singh.

Parampreet Singh

Parampreet Singh with a young student who often asks him the most difficult and so far unanswerable questions on the resolution of singularities. Dr Parampreet Singh is Associate Professor at Department of Physics and Astronomy at Louisiana State University.

Einstein’s theory of classical general relativity breaks down when spacetime curvature
becomes extremely large near the singularities. To answer the fundamental questions
about the origin of our Universe or what happens at the central singularity of the black holes thus lies beyond the validity of Einstein’s theory. Our research deals with discovering the framework which guarantees resolution of singularities.

It has been long expected that quantum gravitational effects tame the classical singularities leading to insights on the above questions. A final theory of quantum gravity is not yet there but the underlying techniques can be used to understand whether quantum gravitational effects resolve cosmological and black hole singularities. Our goal is Continue reading

Tilting laser beams in LISA

by Michael Tröbs.

Michael Troebs in the lab

Michael Tröbs in the lab. Michael Tröbs is an experimental physicist at Max Planck Institute for Gravitational Physics (AEI). The LISA optical bench test bed was built in collaboration with Airbus DS and University of Glasgow. At AEI Michael is responsible for the project.

A testbed to experimentally investigate tilt-to-length coupling for LISA, a gravitational-wave detector in space.

The planned space-based gravitational-wave detector LISA will consist of three satellites in a triangle with million kilometer long laser arms. This constellation will orbit the Sun, following the Earth. LISA is expected to be laser shot-noise limited in its most sensitive frequency band (in the Millihertz range). The second largest contribution to the noise budget is the coupling from laser beam tilt to the interferometric length measurement, which we will call tilt-to-length (TTL) coupling in the following.

How does tilt-to-length coupling come about? Continue reading

Setting space on fire

by Yasaman K. Yazdi and Niayesh Afshordi.

Niayesh Afshordi and Yasaman Yazdi discover that firewalls have consequences

Niayesh Afshordi and Yasaman Yazdi discover that firewalls have consequences. Yasaman K. Yazdi is a PhD candidate at the University of Waterloo and the Perimeter Institute for Theoretical Physics. Niayesh Afshordi is an associate professor at the University of Waterloo and the Perimeter Institute for Theoretical Physics.

Thought experiments highlight the edge of our understanding of our theories.  Sometimes, however, we can get so caught up in heated debates about the solution to a thought experiment, that we may forget that we are talking about physical objects, and that an actual experiment or observation may give the answer.  In this Insight we discuss a proposed solution to the black hole information puzzle, and a possible observational signal that might confirm it.


The black hole information puzzle and a potential solution

The black hole information loss problem is a decades old problem that highlights the tensions between some of the pillars of modern theoretical physics. It has evolved from being Continue reading