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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Interview with Daniela Saadeh: winner of the IOP Gravitational Physics Group (GPG) thesis prize

Daniela Saadeh

Daniela Saadeh – UCL Astrophysics Group

CQG is proud to sponsor the IOP Gravitational Physics Group (GPG) thesis prize. This year the prize was awarded to Daniela Saadeh, who we have interviewed below. Congratulations Daniela!

Can you tell us a little bit about the work in your thesis?

A fundamental assumption of the standard model of cosmology is that the large-scale Universe is isotropic – i.e. that its properties are independent of direction. Historically, this concept stemmed from the Copernican Principle, the philosophical statement that we do not occupy a ‘special’ place in the Universe. In physical terms, this idea is converted into the assumption that all positions and directions in the Universe are equivalent, so that no observer is ‘privileged’.

However, assumptions must be tested, especially foundational ones. General relativity – our standard theory of gravity – allows for many ways in which spacetime could be anisotropic: directional symmetry is not fundamentally required. If the Universe were indeed to be anisotropic, we would actually need to carefully revise our understanding (for instance, calculations about its history or content). Making this health check is very important! Continue reading

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

Going NUTs

By Paul I. Jefremov and Volker Perlick.

Among all known solutions to Einstein’s vacuum field equation the (Taub-)NUT metric is a particularly intriguing one. It is that metric that owing to its counter-intuitive features was once called by Charles Misner “a counter-example to almost anything”. In what follows we give a brief introduction to the NUT black holes, discuss what makes them interesting for a researcher and speculate on how they could be detected should they exist in nature.

paul jefremov-and-volker

Volker Perlick and Pavel (Paul) Ionovič Jefremov from the Gravitational Theory group at the University of Bremen in Germany. Volker is a Privatdozent and his research interests are in classical relativity, (standard and non-standard) electrodynamics and Finsler geometry. He is an amateur astronomer and plays the piano with great enthusiasm and poor skills. Paul got his diploma in Physics at the National Research Nuclear University MEPhI in Moscow, 2014. Now he is a PhD Student in the Erasmus Mundus Joint Doctorate IRAP Programme at the University of Bremen. Beyond the scientific topics in physics his interests include philosophy in general, philosophy of science, Eastern and ancient philosophy, religion, political and social theories and last but not the least organic farming.

The NUT (Newman–Unti–Tamburino) metric was obtained by Newman, Unti and Tamburino (hence its name) in 1963. It describes a black hole which, in addition to the mass parameter (gravito-electric charge) known from the Schwarzschild solution, depends on a “gravito-magnetic charge”, also known as NUT parameter. If the NUT metric is analytically extended, on the other side of the horizon it becomes isometric to a vacuum solution of Einstein’s field equations found by Abraham Taub already in 1951. However, for an observer who is prudent enough to stay outside the black hole, the Taub part is irrelevant.

At first sight, the existence of the NUT metric seems to violate the uniqueness (“no-hair”) theorem of black holes according to which a non-spinning uncharged black hole is uniquely characterised by its mass. Actually, there is no contradiction because Continue reading

Black holes without special relativity

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.

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

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

Pants on fire!

One of the authors, Ian Jubb, discussing a pair of trousers with his colleagues at Imperial College London. Ian Jubb is currently the PhD student of Fay Dowker at Imperial College London.

One of the authors, Ian Jubb, discussing a pair of trousers with his colleagues at Imperial College London. Ian Jubb is currently the PhD student of Fay Dowker in the Theoretical Physics group at Imperial College London.

by Ian Jubb and Michel Buck.

Did you know that Quantum Gravity literally sets pants on fire?

Your pants are not just a nifty garment, they are also a perfect example of a space undergoing a process known as topology change. Take a space that initially consists of two separate circles. If they were to meet and merge into a single circle, the topology of the space would have changed. The trousers allow us to visualise each stage of this process, with cross sections higher up the trouser leg corresponding to later times in the process (if we hold the trousers upside-down, we get the reverse process, corresponding to a single circle splitting into two circles). Instead of viewing this process as the space changing in time, Einstein would tell us to view the trousers in their entirety, as one whole spacetime — the trousers spacetime.

But why should we care about spaces that can ‘split’ and ’attach’ like this? It turns out that there are good reasons to believe that Continue reading