Memories of Professor Stephen Hawking, 1942-2018

by Clifford Will, Editor-in-Chief, Classical and Quantum Gravity

The gravitational physics community, indeed the whole world, mourns the passing on Wednesday 14th March, 2018, of Stephen Hawking at the age of 76. The Editor, Board and staff of CQG offer their heartfelt condolences to Stephen’s family. There are already numerous extended obituaries of Stephen, and I won’t attempt one here (see for example the fine obituaries by Dennis Overbye in the New York Times and by Roger Penrose in the Guardian).

I will, however, offer two personal remembrances of Stephen that I hope will illustrate his humorous side. In 1972, I was a student at the famous Les Houches Summer School on black holes, where Stephen, Brandon Carter and Jim Bardeen lectured and wrote the seminal paper “The Four Laws of Black Hole Mechanics”, that suggested a formal analogy with the laws of thermodynamics. This was soon followed by papers by Jacob Bekenstein and by Stephen that made this more than an analogy. But one of the things I most remember about the school was the awe-struck look on my eight-year-old daughter Betsy’s face watching Stephen in his wheelchair demonstrating how he could wiggle his ears like Dumbo the elephant.

The second remembrance was a visit to Cambridge in 1978, where Stephen had asked me to give a colloquium on tests of GR and invited me and my wife to join him and Jane at “high table” dinner at his college, Gonville and Caius. I showed up in a psychedelic paisley shirt with ridiculously wide collars, baby blue flared jeans, and high-heeled boots (think John Travolta in “Saturday Night Fever”, but with hippie length hair). This was attire totally inappropriate for high table (hey, this was the 70s and was the best I had in my suitcase), but Stephen was delighted to have somebody there who made the stuffy and decorum-obsessed masters of the college more uncomfortable than he did. And when, during the ritual passing of the after-dinner liqueurs along the table, the college master chided me sternly for allowing the port to precede the claret, I thought Stephen was going slide out of his wheelchair, hysterical with laughter.

We have lost a remarkable scientist and a unique human being.

This work is licensed under a Creative Commons Attribution 3.0 Unported License.


Introducing CQG’s 2017 reviewer of the year


Dr Matthew Pitkin is a post-doc at the Institute for Gravitational Research, University of Glasgow and member of LIGO Scientific Collaboration

It’s sophomore year of our Classical and Quantum Gravity reviewer of the year awards. This year congratulations go to Dr Matthew Pitkin whose reviews were not only of exceptional quality but also submitted in good time. Matt has dedicated even more time to CQG by answering these questions. Congratulations Matt!

Tell us how you go about reviewing an article?

I’d probably echo many of last years’ winners points. Firstly, I have to decide whether I think I have the expertise to review the article. Working in the field of gravitational waves, I quite often receive requests to review papers on aspects of theoretical gravity, which I have absolutely no relevant knowledge of. (Going by my day-to-day work I’m really just a self-taught software developer and data scientist, who masquerades as an astrophysicist!) If I decide that I am qualified, then I give the article a quick skim, print it out, write “For review” in big red letters on it, and sit it somewhere prominently on my desk, so that I can’t ignore it.  I also set an online calendar reminder with the deadline for returning the review.

I normally actually sit down to perform the review during a lull in my day-to-day work, like when I’ve just set an analysis code running. I just go through it methodically with a red pen in hand and scribble on the print out when I hit things I don’t understand or think might be problematic. Often, I’ll find that parts I don’t understand are actually explained later on in the paper, so this can indicate that some rearrangement of the article might be in order to clarify things. I check for any stand-out mathematical errors, but don’t have the ability to check all derivations in papers. I try not to make comments for the sake of writing something if there aren’t any problems with the paper. When I do make comments, I try to give constructive advice about how to improve the clarity of the article, or where more explanation might be required. But, I also know that it’s not my job to re-write the article, so don’t give very lengthy comments or suggestions.

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Some features of the Cosmos in Loop Quantum Gravity

By Parampreet Singh, Louisiana State University, USA


CQG Editorial Board member, Param Singh, Guest Edited the Applications of loop quantum gravity to cosmology focus issue in 2016 and 2017

A successful union of Einstein’s general relativity and quantum theory is one of the most fundamental problems of theoretical physics. Though a final theory of quantum gravity is not yet available, its lessons and techniques can already be used to understand  quantization of various spacetimes. Of these, cosmological spacetimes are of special interest. They provide a simpler yet a non-trivial and a highly rich setting to explore detailed implications of quantum gravitational theories. Various conceptual and technical difficulties encountered in understanding quantum dynamics of spacetime in  quantum gravity can be bypassed in such a setting. Further, valuable lessons can be learned for the quantization of more general spacetimes.

In the last decade, progress in loop quantum gravity has provided avenues which allow us to reliably answer various interesting questions about the quantum dynamics of spacetime in the cosmological setting. Quantum gravitational dynamics of cosmological spacetimes obtained using techniques of  loop quantum gravity leads to a novel picture where singularities of Einstein’s theory of general relativity are overcome and a new window opens to test loop quantum gravity effects through astronomical observations.

The scope of the Focus Issue: Applications of loop quantum gravity to cosmology, published last year in CQG, is to provide a snapshot of some of the rigorous and novel results on this research frontier in the cosmological setting.

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How to reach infinity?

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.

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Can You See Asymptotic Symmetries?

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.

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Constructing Spacetimes

By Steven Carlip and Samuel Loomis

Imagine you are given a bucket of points and asked to assemble them into a spacetime. What kind of “glue” would you need?

In causal set theory, the only added ingredient is the set of causal relations, the knowledge of which points are to the past and future of which. In particular, suppose your points were taken at random from a real spacetime, at some typical length scale ℓ. Then on scales large compared to ℓ, the causal diamonds – the sets formed by intersecting the past of one point with the future of another – determine the topology; the causal relations determine the metric up to a scale factor; and the remaining scale factor is just a local volume, which can be obtained by counting points. As the slogan of Rafael Sorkin, the founder of the field, goes, “Order + Number = Geometry.”

Carlip photo

Samuel Loomis and Steven Carlip with their causal set.

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Is Gravity Parity Violating?

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.

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Bouncing a cosmic brew

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.

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A Kind Of Magic

The road from Dunsink to the exceptional symmetries of M-theory

By Leron Borsten and Alessio Marrani 

Our journey starts in the fall of 1843 at the Dunsink Observatory[1], presiding from its hill-top vantage over the westerly reaches of Dublin City, seat to the then Astronomer Royal Sir William Rowan Hamilton. In the preceding months Hamilton had become preoccupied by the observation that multiplication by a complex phase induces a rotation in the Argand plane, revealing an intimate link between two-dimensional Euclidean geometry and the complex numbers ℂ. Fascinated by this unification of geometry and algebra, Hamilton set about the task of constructing a new number system that would do for three dimensions what the complexes did for two. After a series of trying failures, on October 16th 1843, while walking from the Dunsink Observatory to a meeting of the Royal Irish Academy on Dawson Street, Hamilton surmounted his apparent impasse in a moment of inspired clarity: rotations in three dimensions require a four-dimensional algebra with one real and three imaginary units satisfying the fundamental relations i= j= k= ijk = -1. The quaternions ℍ were thus born. Taken in that instant of epiphany, Hamilton etched his now famous equations onto the underside of Broome bridge, a cave painting illuminated not by campfire, but mathematical insight and imagination.  Like all great mathematical expressions, once seen they hang elegant and timeless, eternal patterns in the fixed stars merely chanced upon by our ancestral explorers.


Leron Borsten (left) and Alessio Marrani (right) stood before Hamilton’s fundamental relations, Broome bridge Dublin. Leron is currently a Schrödinger Fellow in the School of Theoretical Physics, Dublin Institute for Advanced Studies. Alessio is currently a Senior Grantee at the Enrico Fermi Research Centre, Roma.

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Black and White Hole Twins Connected by Quantum Gravity

By Javier Olmedo, Sahil Saini and Parampreet Singh

Black holes are perhaps the most exotic objects in our Universe with very intriguing properties. The event horizon does not allow light and matter to escape, and hides the central singularity. As in the case of the big bang singularity, the central singularity is a strong curvature singularity where all in-falling objects are annihilated irrespective of their strength. Since singularities point out pathologies of general relativity, a more fundamental description obtained from quantum gravity must resolve the problem of singularities. Singularity resolution is also important for resolving many of the paradoxes and conundrums that plague the classical theory such as the cosmic censorship conjecture, black hole evaporation, black hole information loss paradox, etc.

Black holes have mirror versions too. Known as white holes, these are solutions of general relativity with the same spacetime metric.  If the black holes do not allow even the light to escape once it enters the horizon, thus nothing can enter the white hole horizon. Light and matter can only escape from the white hole. It has sometimes been speculated that black hole and white hole solutions can be connected, providing gateways between different universes or travelling within the same universe, but details have been sparse. The reason is due to the presence of the central singularity which does not allow a bridge between the black and white holes. Continue reading