The possible emptiness of a final theory

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

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?

J M Grimstrup

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.

img_0192This algebra, which we call the quantum holonomy-diffeomorphism (QHD) algebra [1], is interesting for two reasons Continue reading

CQG+ Insight: The problem of perturbative charged massive scalar field in the Kerr-Newman-(anti) de Sitter black hole background

Written by Dr Georgios V Kraniotis, a theoretical physicist at the University of
Ioannina in the physics department.

Solving in closed form the Klein-Gordon-Fock equation on curved black hole spacetimes

Georgios Kraniotis

Dr Georgios V Kraniotis (University of Ioannina)

A new exciting era in the exploration of spacetime
The investigation of the interaction of a scalar particle with the gravitational field is of importance in the attempts to construct quantum theories on curved spacetime backgrounds. The general relativistic form that models such interaction is the so called Klein-Gordon-Fock (KGF) wave equation named after its three independent inventors. The discovery of a Higgs-like scalar particle at CERN in conjuction with the recent spectacular observation of gravitational waves (GW) from the binary black hole mergers GW150914 and GW151226 by LIGO collaboration, adds a further impetus for probing the interaction of scalar degrees of freedom with the strong gravitational field of a black hole.

Kerr black hole perturbations and the separation of the Dirac’s equations was a central theme in the investigations of Teukolsky and Chandrasekhar [1].

All the above motivated our research recently published in CQG on the scalar charged massive field perturbations for the most general four dimensional curved spacetime background of a rotating, charged black hole, in the presence of the cosmological constant \Lambda [2].

Where interesting physics meets profound mathematics
The KGF equation is the relativistic version of the Schrödinger equation and thus is one of the fundamental equations in physics.

In our recent CQG paper, we examined Continue reading

CQG+ Insight: More Classical Charges for Black Holes

Written by Geoffrey Compère, a Research Associate at the Université Libre de Bruxelles. He has contributed to the theory of asymptotic symmetries, the techniques of solution generation in supergravity, the Kerr/CFT correspondence and is generally interested in gravity, black hole physics and string theory.

Why mass and angular momentum might not be enough to characterize a stationary black hole

Geoffrey Compère

Geoffrey Compère having family time in the park Le
Cinquantenaire in Brussels.

“Black hole have no hair.” This famous quote originates from John Wheeler in the sixties. In other words, a stationary black hole in general relativity is only characterized by its mass and angular momentum. This is because multipole moments of the gravitational field are sources for gravitational waves which radiate the multipoles away and only the last two conserved quantities, mass and angular momentum, remain. That’s the standard story.

Now, besides gravitational waves, general relativity contains another physical phenomenon which does not exist in Newtonian theory: the memory effect. It was discovered beyond the Iron Curtain by Zeldovich and Polnarev in the seventies and rediscovered in the western world and further extended by Christodoulou in the nineties. While gravitational waves lead to spacetime oscillations, the memory effect leads to a finite permanent displacement of test observers in spacetime. The effect exists for any value of the cosmological constant but in asymptotically flat spacetimes, it can be understood in terms of an asymptotic diffeomorphism known as a BMS supertranslation.

In order to understand that, let’s go back to the sixties where the radiative properties of sources were explored in general relativity; it was found by Bondi, van der Burg, Mezner and Sachs that there is a fundamental ambiguity in the coordinate frame at null infinity. Most expected that Continue reading

CQG+ Insight: Spacetime near an extreme black hole

Written by James Lucietti, a Lecturer in Mathematical Physics in the School of Mathematics at the University of Edinburgh; and Carmen Li, previously a graduate student in the School of Mathematics at the University of Edinburgh and now a postdoc in the Institute of Theoretical Physics at the University of Warsaw.

How many extreme black holes are there with a given throat geometry?


James Lucietti, University of Edinburgh

The classification of equilibrium black hole states is a major open problem in higher dimensional general relativity. Besides being of intrinsic interest, it has numerous applications in modern approaches to quantum gravity and high energy physics. Two key questions to be answered are: What are the possible topologies and symmetries of a black hole spacetime? What is the ‘moduli’ space of black hole solutions with a given topology and symmetry? For vacuum gravity in four spacetime dimensions, these questions are answered by the celebrated no-hair theorem which reveals a surprisingly simple answer: the Kerr solution is the only possibility. However, since Emparan and Reall’s discovery of the black ring — an asymptotically flat five dimensional black hole with ‘doughnut’ topology — it has become clear that there is a far richer set of black hole solutions to the higher dimensional Einstein equations.


Carmen Li, University of Warsaw, at the top of Ben Nevis in the UK.

Over the last decade, a number of general results have been derived which Continue reading

CQG+ Insight: Spectral Cauchy Characteristic Extraction of strain, news and gravitational radiation flux

Written by Casey Handmer, a postdoctoral scholar at the California Institute of Technology. Bela Szilagyi is a researcher at NASA’s Jet Propulsion Laboratory. Jeffrey Winicour is a professor at the University of Pittsburg. Find out more on their group website at

Casey Handmer (postdoctoral scholar at Caltech), Bela Szilagyi (researcher at JPL) and Jeffrey Winicour (professor at Pittsburg) reprise their former stance discussing asymptotically time-like inertial scri+ foliations, now with even better CGI. Image credit: Photo manipulation by Annie Handmer, background image by SXS Collaboration: Andy Bohn et al 2015 Class. Quantum Grav. 32 065002.

Casey Handmer (Caltech), Bela Szilagyi (JPL) and Jeffrey Winicour (Pittsburg) reprise their former stance discussing asymptotically time-like inertial scri+ foliations, now with even better CGI. Image credit: Photo manipulation by Annie Handmer, background image by SXS Collaboration: Andy Bohn et al 2015 Class. Quantum Grav. 32 065002.

Gravitational waves were detected in 2015. GW150914 wiggled LIGO’s mirrors and shook the whole world, except perhaps Stockholm. The opening paragraph of our previous CQG+ article was rendered obsolete:

“Colliding black holes create powerful ripples in spacetime. Of this we are certain. Directly detecting these ripples, or gravitational waves, is one of the hardest unsolved problems in physics.”

That article presented the evolution algorithm that simulates gravitational waves from compact object binaries in computational general relativity. The evolution algorithm is the powerful engine that drives the present work: extraction of all radiative energy-momentum flux in addition to the usual strain and gravitational news.

How did this come about? At APS April 2014, my coauthor Bela and I were approached by Jeffrey Winicour: Bela’s doctoral advisor and, we learned, a referee of our first paper. He excitably described how we could use our evolution algorithm to compute the gravitational wave flux. I schemed to co-opt all other possible referees in the same way.

What is the flux? The ten Poincaré symmetries of asymptotically flat spacetime generate respective conserved Noether momenta: linear momentum, angular momentum, energy, and three boost momenta corresponding to Lorentz transforms. Supertranslations, a possible solution to the Firewall Paradox, also generate momenta that are calculated using this method.

Along the way we discovered a number of surprises. Did you know that spherical foliations of future null infinity in inertial coordinates are actually asymptotically time-like? Read more in our CQG paper.

Read the full article in Classical and Quantum Gravity:
Spectral Cauchy characteristic extraction of strain, news and gravitational radiation flux
Casey J Handmer et al 2016 Class. Quantum Grav. 33 225007

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CQG+ Insight: Scalar-tensor cosmology: inflation and invariants

Written by Piret Kuusk, Mihkel Rünkla, Margus Saal, Ott Vilson, researchers from the Institute of Physics at the University of Tartu, Estonia.

The authors in front of the building of the Institute of Physics, University of Tartu, Estonia: doctoral students Mihkel Rünkla (far left), Ott Vilson (far right), senior researcher Margus Saal (center left), head of the Laboratory of Theoretical Physics Piret Kuusk (center right).

The authors in front of the building of the Institute of Physics, University of Tartu, Estonia: doctoral students Mihkel Rünkla (far left), Ott Vilson (far right), senior researcher Margus Saal (center left), head of the Laboratory of Theoretical Physics Piret Kuusk (center right).

Working in the field of cosmology one deals casually with modified gravity. Modifications can be small or large. Sometimes a small modification of the theory could cause a large effect. It is also possible that large modifications do not affect the predictions of the theory at all. The concept of cosmological inflation can probably illustrate both of these situations somehow. Adding a short period of inflation to the evolution of early universe seems as a small modification of the theory. This modification in turn has a large effect as it solves the horizon and flatness problems. In the simplest case inflation is driven by an additional scalar field with a suitable self-interaction potential. During inflation potential dominates over the kinetic term of the scalar field giving rise to a slow roll. Dealing with slow-roll inflation can illustrate the second aforementioned situation: slow-roll can be incorporated in different theoretical frameworks not affecting the universal predictions of slow-roll.

Although the predictions of slow-roll inflation are in some sense universal, the observational data can still invalidate some specific models. One can read sentences as “minimally coupled inflation is ruled out”, which invite us to consider Continue reading

CQG+ Insight: Playing with the building blocks of space

Daniele Oriti is a senior researcher and group leader at the Max Planck Institute of Gravitational Physics (Albert Einstein Institute) in Potsdam, Germany, EU. Born and educated in Italy, got a PhD from the University of Cambridge, UK, and held research position at Cambridge, Utrecht University, The Netherlands, and the Perimeter Institute for Theoretical Physics, Canada. He lives and plays with physics, philosophy, and the rest of the universe, in Berlin, with his wife and son.

In this Insight, the fundamental building blocks of quantum spacetime are described by peculiar quantum field theories, then assembled to form continuum geometries, to explain the dynamics of the early universe and black holes from first principles.

Daniele Oriti

Daniele Oriti is a senior researcher and group leader at the Max Planck Institute of Gravitational Physics (Albert Einstein Institute) in Potsdam, Germany.

What is space made of? What are its fundamental building blocks? Can we play with them? And what can we make out of them?

If these sound like a bunch of childish questions, it is because theoretical physicists manage to remain the children they once were for some time longer; and to make a living by asking childish questions and playing with the mathematical toys that accompany them.

The serious, only-for-adults part of the story is that we have learned from General Relativity that space and time are physical entities, so it is actually reasonable to ask if they have a microstructure. Moreover, we have several hints (e.g from black hole physics and cosmological singularities) that the continuum geometric description of spacetime on which General Relativity is based should give way to one in terms of discrete, non-geometric degrees of freedom. This is the goal of quantum gravity: a quantum theory of the microstructure of space and time, to understand their discrete non-geometric building blocks and how the usual continuum description arises in some approximation.

Modern approaches to quantum gravity are achieving just that. Loop quantum gravity, for example, identifies spin networks as the structures underlying space (and their interaction processes, spin foams, as underlying spacetime): purely combinatorial objects, graphs, labeled by algebraic data, i.e. group representations. The continuum world populated by Continue reading

CQG+ Insight: Chiral Gravity

by Kirill Krasnov

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

A Study of Time Delay from Different Time Zones

Netta Engelhardt (University of California, Santa Barbara) and Sebastian Fischetti (Imperial College) gave us an insight into their communication methods whilst collaborating for their research paper recently published in CQG.


On a dark London evening and a sunny California day — January 19, 2016, to be precise — Netta sent Sebastian a Skype message:


So began a new project for this dynamic duo, published recently in CQG. Unlike our previous project, this one presented a new challenge (with which researchers are all too familiar): we were separated by an eight-hour time difference. Thus began a three-way collaboration: Netta, Sebastian, and Skype (with the third member being the least cooperative).

The process began Continue reading

Inspiral into Gargantua; where science meets science-fiction

Niels Warburton from the Massachusetts Institute of Technology shares an insight into his latest work with Sam Gralla and Scott Hughes published in Classical and Quantum Gravity.

Niels Warburton

Niels Warburton is a Marie Curie postdoctoral fellow currently working at the Kavli Institute for Astrophysics and Space Research at the Massachusetts Institute of Technology. He works on calculating gravitational waveforms from the capture of compact objects by black holes ranging from hundreds to millions of solar masses. Outside of research he often encounters other types of waves on the waters around Boston where he is a keen sailor. Niels co-authored the article recently published in CQG with Sam Gralla of the University of Arizona and Scott Hughes at the Massachusetts Institute of Technology.

The first merging black holes recently detected by LIGO were strange objects indeed. Torturing reality so that even light cannot escape from their interiors, as they whirled around each other at over half the speed of light, the disturbances they induced in space and time propagated outwards as gravitational waves. The measured characteristic chirp, an upsweep in frequency and amplitude of the waves, signaled that the two black holes had merged into a single, larger black hole. Amazingly, though this remnant was more than sixty times as massive as our sun it could be described by just two numbers – its mass and its spin. This is an unusual property for any macroscopic object as they usually require Continue reading