Pauli defuses the fermionic black-hole bomb

Fermionic vacuum around Kerr black holes spontaneously decays to form a co-rotating Fermi sea.

Antonin Coutant and Peter Millington

With the direct observation of gravitational waves produced in black-hole and neutron-star mergers by LIGO (the Laser Interferometry Gravitational-Wave Observatory), we have entered an exciting new era of multi-messenger astronomy.  For the first time, we are able to determine the properties of some of the most violent events in our universe, testing our theories of gravity and particle physics in extreme regimes.

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Antonin Coutant is a post-doctoral fellow in the Acoustic Laboratory of Le Mans University

We often think of black holes as giant sinks, which swallow up anything that passes nearby and from which nothing can escape.  However, this picture is not quite right, as Stephen Hawking and others have shown.  In 1971, Roger Penrose discovered a process that allows rotational energy to be extracted from black holes.  Most astrophysical black holes are expected to spin on their axes, due to their formation from the collapse of initially asymmetric or rotating matter distributions.  Understanding how these black holes lose angular momentum is of major interest for gravitational-wave astrophysics and, at the same time, can provide constraints on new models of fundamental physics. A peculiar process of angular-momentum loss is induced by the quantum vacuum of fermionic particles: a co-rotating sea of fermions forms spontaneously around the black hole, extracting some of its rotational energy.

Rotating black holes are described theoretically by the Kerr metric, after Roy Kerr, who found this solution to Albert Einstein’s equations of General Relativity in 1963.  One peculiarity of this solution is the existence of the ergoregion, where physical objects are forced to co-rotate with the black hole.  To extract the black hole’s rotational energy and angular momentum, the Penrose process exploits the unusual properties of the ergoregion.  Specifically, a classical particle incident on the ergoregion can back-scatter inelastically, with the ejected particle having an increased energy.  For scattering waves, a similar process leads to the phenomenon of superradiance: an incident wave can be back-scattered with increased amplitude.  This effect has recently been observed in a water-wave analogue.  Now, if we can arrange for the reflected wave to be directed back towards the black hole after each back-scatter, its amplitude will grow exponentially.

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Peter Millington is a Research Fellow in the Particle Cosmology Group at the University of Nottingham.

In quantum theory, massive particles also behave as waves, and massive particles can become trapped near black holes.  A scalar field (describing a spin-zero boson), with Compton wavelength comparable to the size of the black hole, will scatter in the ergoregion and undergo superradiance.  Modes that are trapped near the black hole can then scatter repeatedly, leading to an instability known as the black-hole bomb.  If such light scalar fields exist in nature, this instability affects the population density of certain angular momenta of black holes, allowing observations to set limits on the masses of these fields.

The black-hole bomb instability cannot occur for fermionic fields (having half-integer spin), due to Wolfgang Pauli’s exclusion principle, which prevents more than one fermion being in any given state.  However, rotating black holes emit a steady radiation of massless fermions in the same frequency range as superradiance would be expected for bosons.  This is known as the UnruhStarobinsky radiation, discovered by William Unruh and Alexei Starobinsky.  When the fermions are massive, the steady radiation is replaced by an instability, corresponding to the decay of the quantum vacuum to a non-trivial state: the Kerr-Fermi sea, where certain fermion modes that co-rotate with the black hole are populated by extracting its rotational energy and angular momentum.

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Introducing CQG’s new Editor-in-Chief

I am very honored to assume the position of Editor-in-Chief of Classical and Quantum Gravity, following ten very successful years by Clifford Will.

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Gabriela González, CQG’s new Editor-in-Chief, is a professor at Louisiana State University and a member of the LIGO Scientific Collaboration

During Cliff’s term, there were very exciting developments in the field, including precision cosmology, new astrophysics and discoveries of gravitational waves – and the journal was there to provide insight and quality articles. The journal has now 15 “renowned” papers with more than 500 citations (according to inspirehep.net), with half of those in the last 10 years, in topics ranging from “Holographic methods for condensed matter physics”, “Loop Quantum Cosmology”, to details of the LIGO and Virgo gravitational detectors and their discoveries. It is this diversity of topics which has made the journal a pillar of the community, thanks to the efforts of the Editor-in-Chief, the Editorial Board, and the excellent IOP editorial team (Adam Day, 2009-2017 and Holly Young until 2019). This is quantified in the journal impact factor, which is very competitive, as well as in the fast turn-around for reviewing and publishing.

There have been many changes in the last decade which have all helped this success: the introduction of focus sections (not just issues), brief review articles, reviewer awards, an open access policy, and an advisory panel, among others. Following the times, Classical and Quantum Gravity has a presence in social media, especially through this CQG+ blog, started by Adam Day.  The journal has also acquired a physical presence in many conferences in the field to keep in touch with latest developments, and sponsors two important awards for young scientists, the IOP Gravitational Physics Group Thesis prize and the ISGRG Bergmann–Wheeler Thesis Prize. The journal prides itself on having very diverse article authors, with diversity understood in the broadest sense: geography, gender, age, and expertise area among others.

I am very humbled to occupy a position that six eminent scientists held before (H. Nicolai, G. Gibbons, K. Stelle, M. MacCallum, R. Wald and C. Will), and will help the journal continue to grow and succeed in a rapidly evolving field. It is my goal to maintain the highest standards for the journal, as we broaden the range of articles – “gravity” is at the core of exciting theory and experiment with expanding frontiers at cosmologically large and small quantum scales.

Professor Gabriela González

Changes afoot

Happy New Year (is it too late to say that?) from the whole team here at Classical and Quantum Gravity and CQG+.

We’re starting the new year with an injection of fresh blood. Due to a bit of reshuffle at IOP Publishing, I (Holly) will be moving teams to work on our biophysics titles. As a result of this, Benjamin Sheard will be taking over as Publisher of CQG. Ben is already very familiar with CQG having worked on it for quite some time a couple of years ago, so his name might be familiar to you.

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Out with the old, in with the new

You might also start seeing some new faces around these parts as a new editorial operations team takes over to manage CQG peer review, many CQG+ invitations and the journal mailbox.

I’d like to take this opportunity to thank everyone who has supported the journal and our little blog here. I’ve only been working on it for a couple of years, but it’s been an absolute pleasure to work with everyone I’ve encountered. A particular note of thanks goes to the CQG Editorial Board and our Guest Editors who have contributed so much to the journals’ success and made my job that much easier.

I know that all of you will welcome Ben (back) to the community, so be sure to stop by the IOP Publishing stand at your next conference and say hello!

Stay tuned for our next announcement … it’s a big one!


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

How the Tiger got its Stripes

By Nicolas Yunes, Stephon Alexander, and Kent Yagi


Nature is sometimes lazy and messy, like a 4 year-old that likes to play with all of the toys and put none of them away, always increasing the degree of disorder. In physics, we quantify disorder through the concept of entropy. The tendency of systems to always increase their entropy is encoded in the second law of thermodynamics. Aside from a kid’s disorganised bedroom, another place in the universe with a tremendous amount of entropy is a black hole. Bekenstein and Hawking [1-4] proved that the entropy of a black hole in General Relativity is proportional to its area. For astrophysical black holes of stellar-mass, this yields a value of entropy of about 1056 Joules per Kelvin. The reason for this large value is their incredibly small temperature, about 10-9 Kelvin for a stellar-mass black hole, which in fact cannot be any smaller for an object of its size due to Heisenberg’s uncertainty principle.

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Yunes is an Associate Professor of Physics at Montana State University and co-founder of the eXtreme Gravity Institute.

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Alexander is a Professor of Physics at Brown University.

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Yagi is an Assistant Professor of Physics at the University of Virginia.

The entropy area scaling is surprising because the entropy of extensive systems in statistical mechanics is proportional to their volume, not their area. In fact, Bekenstein’s and Hawking’s observation was a strong motivator for the concept of holography. The typical rationalisation of the area result is that black holes are special objects because, by definition, they possess a horizon. The argument is then that the entropy is proportional to the area because somehow the internal degrees of freedom of a black hole are imprinted on the surface area associated with its horizon. The consequence of this argument is that the only objects in nature whose entropy scales with their surface area are those with event horizons. In particular, the entropy of stars, be them compact or not, should scale with their volume and not their area. Continue reading

Quantum imprints of a black hole’s shape

Can quantum fields tell us about the curvature of a black hole event horizon?

By Tom Morley,  Peter Taylor, Elizabeth Winstanley


The event horizon of a black hole completely surrounds a singularity. It seems obvious that the event horizon takes the form of a (possibly distorted) sphere, a surface with positive curvature. If the space-time far from the black hole is flat, this must be the case. Suppose instead that the space-time in which the black hole is situated itself has negative curvature (this is known as anti-de Sitter space-time and arises in string theory). Then the event horizon does not have to have positive curvature; it can have zero or negative curvature.

How do these different horizon shapes affect black hole physics? If we look at our reflection in a flat mirror, it is undistorted, but a mirror with positive or negative curvature distorts our reflection, as might be experienced in a “hall of mirrors” at a fairground (see image below for some similar effects).

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Tom Morley is a PhD student at the University of Sheffield.

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Peter Taylor is Assistant Professor of Mathematical Sciences at the Centre for Astrophysics and Relativity, Dublin City University.

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Elizabeth Winstanley is Professor of Mathematical Physics at the University of Sheffield.

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Space Is the Place*

How to master spatial average properties of the Universe?

by Thomas Buchert, Pierre Mourier & Xavier Roy.


The question of how to define a cosmological model within General Relativity without symmetry assumptions or approximations can be approached by spatially averaging the scalar parts of Einstein’s equations. This yields general balance equations for average properties of the Universe.  One open issue that we address here is whether the form and solutions of these equations depend on the way we split spacetime into spatial sections and a global cosmological time. We also discuss whether we can at all achieve this – given the generality of possible spacetime splits.

Our CQG Letter explores the general setting with a surprisingly simple answer.

Currently most researchers in cosmology build model universes with a simplifying principle that is almost as old as General Relativity itself.  One selects solutions that are isotropic about every point, so that no properties of the model universe depend on direction. This local assumption restricts one to homogeneous geometries that define the cosmological model globally, up to the topology that is specified by initial conditions. Spacetime is foliated into hypersurfaces of constant spatial curvature, labelled by a global cosmological time-parameter. The homogeneous fluid content of these model universes is assumed to define a congruence of fundamental observers moving in time along the normal to these hypersurfaces. Einstein’s equations reduce, in this flow-orthogonal foliation, to the equations of Friedmann and Lemaître. The only gravitational degree of freedom is encoded in a time-dependent scale factor, which measures the expansion of space. Continue reading

Constructing AdS-like spacetimes

By Diego A. Carranza and Juan A. Valiente Kroon


Maldacena’s AdS-CFT correspondence has brought the study of properties of anti de Sitter-like spacetimes (AdS spacetimes for short) to the centre of attention of a wide community of researchers. This class of spacetimes is characterised by a time-like conformal boundary similar to that of the anti-de Sitter spacetime. Maldacena’s correspondence relates AdS spacetimes to dual conformal field theories defined on the boundary of the spacetime. In particular, it allows to obtain information otherwise not easily accessible about the conformal field theories through the numerical computation of the dual spacetime. Thus, numerical simulations of these spacetimes have received a substantial amount of attention in recent years.  The existence of the time-like conformal boundary in these spacetimes also has implications of interest to mathematicians studying general properties of solutions to the Einstein equations. AdS spacetimes are examples of non-globally hyperbolic solutions to the Einstein field equations. Accordingly, if one wants to formulate a well-posed initial value problem for an AdS spacetime, in addition to the initial data, it is necessary to provide some information on the boundary. The prescription of boundary data is linked to the question of stability of this kind of solutions to the Einstein equations as, during the last years, numerical evidence has showed that under certain boundary conditions the anti-de Sitter spacetime is unstable under non-linear perturbations.

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A Successful Eccentric

by Blake Moore

Humankind has been obsessed with circles for a long time. It comes as no surprise then that the modeling of gravitational waves had focused until recently on those emitted by black holes or neutron stars in circular orbits around each other. But in the case of gravitational wave modeling, there is good reason for this obsession. Gravitational waves remove energy and angular momentum from a binary, forcing the eccentricity to decay and the orbit to circularize rapidly. Since the 1960s, the expectation has then been that the gravitational waves that ground-based detectors would observe would correspond to circular binaries.

Travis, Blake and David at Yellowstone

Travis Robson (right), Blake Moore (center), and David Anderson (left) are members of the eXtreme Gravity Institute at Montana State University. Here they are at nearby Yellowstone National Park.

But as with most things in physics, Nature adores the complex if one looks closely enough. Several astrophysical studies have recently shown that binaries may form with moderate eccentricities at orbital separations at which they would be emitting gravitational waves that ground-based detectors could observe very soon. These binaries would form near a supermassive black hole or in globular clusters, where three- or many-body interactions may source eccentricity. And if they are detected, they could shed light on their true population and formation scenario.

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Building modified theories of gravity from models of quantum spacetime

Hints from non-commutative geometry


By Marco de Cesare, Mairi Sakellariadou, and Patrizia Vitale 


It is often argued that modifications of general relativity can potentially explain the properties of the gravitational field on large scales without the need to postulate a (so far unobserved) dark sector. However, the theory space seems to be virtually unconstrained. One may then legitimately ask whether there is any guiding principle —such as symmetry— that can be invoked to build such a modified gravity theory and ground it in fundamental physics. We also know that the classical picture of spacetime as a Riemannian manifold must be abandoned at the Planck scale. The question then arises as to what kind of geometric structures may replace it, and if there are any novel gravitational degrees of freedom that they bring along. Importantly, one may ask whether there are any potentially observable effects away from the experimentally inaccessible Planck regime. These questions are crucial both from the point of view of quantum gravity and for model building in cosmology; trying to answer them will help us in the attempt to bridge the gap between the two fields, and could have far-reaching implications for our understanding of the quantum structure of spacetime.

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Gravitation in terms of observables: breathing new life into a bold proposal of Mandelstam

By Rodolfo Gambini and Jorge Pullin


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Rodolfo Gambini and Jorge Pullin have been collaborating for 27 years

In the 1960’s Stanley Mandelstam set out to reformulate gravity and gauge theories in terms of observable quantities. The quantities he chose are curves, but specified intrinsically. The simplest way of understanding what does “specified intrinsically” means is to think how the trajectory of a car is specified by a GPS unit. The unit will give commands “turn right”, “advance a certain amount”, “turn left”. In this context “right” and “left” are not with respect to an external coordinate system, but with respect to your car. The list of commands would remain the same whatever external coordinate system one chooses (in the case of a car it could be a road marked in kilometres or miles, for instance). The resulting theories are therefore automatically invariant under coordinate transformations (invariant under diffeomorphisms). They can therefore constitute a point of departure for the quantization of gravity radically different from other ones. For instance, they would share in common with loop quantum gravity that both are loop-based approaches. However, in loop quantum gravity one has to implement the symmetry of the theory under diffeomorphisms. Intrinsically defined loops, on the other hand, are space-time diffeomorphism invariant, therefore such a symmetry is already implemented. It is well known that in loop quantum gravity diffeomorphism invariance is key in selecting in almost unique way the inner product of the theory and therefore on determining the theory’s Hilbert space. Intrinsically defined loops are likely to be endowed with a very different inner product and Hilbert space structure. In fact, since the loops in the Mandelstam approach are space-time ones it lends itself naturally to an algebraic space-time covariant form of quantization. Continue reading