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.


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.


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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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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Soft hair and you

by Josh Kirklin

Awaken, quantum relativist.

Have breakfast, and notice that a black hole has found its way into your laboratory. You measure its mass M, electric charge Q and angular momentum J, double-check the statement of the no hair theorem, and tell yourself that you can learn no more about this particular black hole.

But the quantum mechanic inside of you objects. As a devout believer in unitarity, you are convinced that the black hole must contain a complete description of the matter involved in its formation. So, you think, the no hair theorem must not apply. Finding no logical inconsistency in the mathematical steps involved in its proof, you decide that something must be wrong with its initial assumptions.

One such assumption is that two black holes related by a gauge transformation are physically equivalent. But this cannot be correct, since if we do a gauge transformation whose action does not vanish sufficiently quickly at infinity, there are observable consequences. The quickest way to become convinced of this fact is to find the Poisson brackets appropriate for a description of gravity and electromagnetism, and to use them to compute the actions generated by M, Q and J. The action of each is a gauge transformation that is non-trivial at infinity, and it is a basic fact of Hamiltonian mechanics that if a quantity is observable (M, Q and J certainly are), then so too must be the action that it generates.


About the author: Josh Kirklin is a PhD student in the Relativity and Gravitation group at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge. He studies black hole thermodynamics and the role of information in quantum gravity.

You deduce that you have at least three new gauge-dependent observable parameters (one for each of M, Q and J) to describe your black hole. In fact, you have infinitely many more, since the dipole, quadrupole and higher order moments of M, Q and J also generate gauge transformations that are non-trivial at infinity. The no hair theorem guarantees that the higher order moments of M, Q and J themselves must vanish, but it does not claim the same for the resultant new gauge-dependent variables.

So you conclude that your stationary black hole is actually described by infinitely many degrees of freedom. These are known as soft hairs, and the quantities which generate their transformations are known as soft charges.

During lunch, you manage to devise a clever experiment which makes use of the gravitational and electromagnetic memory effects to measure the soft hairdo of your black hole. Partially out of respect for the event horizon, but mostly out of fear, you decide to stay far enough away from the black hole that you must treat yourself as an idealised observer at infinity in your calculations. So, carrying out your experiment, you obtain a set of numbers describing how the soft hair appears to an observer at infinity.

But the black hole is an isolated body in spacetime, whose properties should be intrinisic to it. What you really desire is a description of the soft hair that is local to the black hole – one that would reflect what a more courageous observer, who was more willing to closely approach the event horizon, might see. You wonder what the best way would be to deduce such a local description from your observations at infinity, and, absent-mindedly leafing through the latest issue of CQG, you stumble upon a paper that takes you part of the way towards the answer. Following its advice, you are able to write the soft charges in terms of fields close to the black hole.

At dinner, you decide that you would like to justify your scientific credentials by predicting the future of the black hole. Before the discovery of soft hair, you would have only been able to treat the black hole as a single thermodynamical system, supporting an entropy and emitting Hawking radiation. This was necessary because you only had a macroscopic description for your black hole, being ignorant of its microscopic physics. But now you feel that you can improve on this, since you have a candidate for the black hole’s microscopic degrees of freedom – its soft hair. To make some predictions, all you need is a theory that governs the dynamics of the soft hair, and that same paper seems to again provide some assistance. It argues that a softly hairy black hole should actually be treated as an infinity of thermodynamic systems, all in thermal contact with each other. This thermal contact manifests as a heat current on the event horizon.

You use these results to make your predictions, and climb into bed after an exhausting day of hands-on relativity. Drifting off to sleep, you wonder whether the discovery of soft hair will be enough to solve one of the biggest mysteries of black hole physics – the information paradox. To have any hope of this being the case, you ought to be able to use the existence of soft hair to derive the black hole area entropy relation. You have heard rumors that this result is close at hand, and that the paper announcing it will bear Stephen Hawking’s name (making it his last published work).

Until then, you can only dream of tomorrow’s meals and measurements…

Read the full article in Classical and Quantum Gravity:                                                     Localisation of soft charges, and thermodynamics of softly hairy black holes
Josh Kirklin,
2018 Class. Quantum Grav. 35 175010

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Putting a limit on the mass of the graviton

by Clifford Will


Clifford Will ( is Distinguished Professor of Physics at the University of Florida and Chercheur Associé at the Institut d’Astrophysique de Paris. Until the end of 2018, he is Editor-in-Chief of CQG.

According to general relativity, the gravitational interaction is propagated as if the field were massless, just as in electrodynamics.   Thus the speed of gravitational waves is precisely the same as the speed of light, a fact spectacularly confirmed when gravitational waves and gamma rays from the binary neutron star merger event GW170817 arrived within 1.74 seconds of each other, even after traveling for 120 million years.

But some modified gravity theories propose that the field could be massive, so that gravitational waves might propagate more slowly than light, and with a speed that depends on wavelength.   The shorthand term for this is a “massive graviton”, although quantum gravity plays no role in this discussion.  This is entirely a classical phenomenon.

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Low Energy? Think Positive!

Scott Melville, winner of the Best Student Talk Prize at BritGrav, which was sponsored by CQG, discusses the research that he’s doing on quantum gravity at Imperial College London.

Image courtesy of Steve Cross

Scott Melville, speaking at Bright Club on 28th April 2018. Image courtesy of Steve Cross

The present state of quantum gravity is rather unsatisfying. While perturbation theory works well at low energies, at high energies quantum gravity becomes incalculable, and leaves us hungry for answers. As we approach the Planck scale, perturbations become strongly coupled and we quickly lose perturbative control of our theory. A UV complete theory of gravity, which remains unitary and sensible to arbitrarily high energies, is hard to cook up.

We need new physics, to swallow these Planck-sized problems. This new physics shouldn’t be too heavy, or too light; not too strongly coupled, or too perturbative. We don’t yet know exactly what it should be, but it needs to hit a sweet spot. My research develops tools, called positivity bounds, which can help us better understand how low energy observables are connected to this unknown new physics.

One thing is for certain: quantum gravity is hard – and working on it sure builds up an appetite. When I’m not worrying about the fundamental nature of the Universe: I’m in the kitchen. While I may not be the best chef in the world, I make up for an abysmal lack of skill with a towering surplus of enthusiasm. You can flip anything in a pan, if you flip hard enough.

When it comes to deciding what to have for dinner, I take things very seriously: it can’t be too salty, or too sweet; not too spicy, or too bland.

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A good month for Einstein – gravitational starlight deflection during the Great American Eclipse

by Dr. Donald G. Bruns


Don Bruns and his wife Carol on eclipse day at the Lions Camp on Casper Mtn. The tripod is bolted to the custom mosaic designed and built by his cousin Steve Lang.

After much anticipation, two experiments had great successes last year.  On August 17 2017, the LIGO/VIRGO collaboration monitored the merger of two neutron stars millions of light years away.  Only four days later in Wyoming, an experiment to measure the gravitational bending of starlight by the Sun acquired the best data since the idea was first tested in 1919, by Sir Arthur Eddington, in Africa.  I published my results on that experiment in Classical and Quantum Gravity on March 6, 2018.  My solo project to repeat Eddington’s achievement, which made Einstein famous, required a lot less manpower than LIGO!

Early last century, Einstein published his General Theory of Relativity that contained some unusual predictions, including the idea that massive bodies bend light beams.  The only way to test this would be during a total eclipse, when the sky would be dark enough to see stars close to the Sun, where the effect just might be measurable.

I started planning Eddington’s re-enactment when I found out that no one had attempted it since 1973 (also in Africa) and that no one had ever succeeded in getting all the parts to work during those precious few minutes of totality.  I assumed that with modern charge-coupled device (CCD) cameras and computerized telescopes, the experiment would be much easier.  I was wrong!  While some aspects were simplified (the Gaia star catalog provided accurate star positions, for example, and modern weather predictions and the compact equipment eased many logistics problems), dealing with pixels, turbulence, and a limited sensor dynamic range presented new challenges.

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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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Tails of gravitational waves and mechanics of compact binaries

by Luc Blanchet and Alexandre Le Tiec

The first law of binary black hole mechanics can be extended to include non local tail effects.

Ever since Kepler’s discovery of the laws of planetary motion, the “two-body problem” has always played a central role in gravitational physics. In Einstein’s general theory of relativity, the simplest and most “universal,” purely gravitational, two-body problem is that of a binary system of black holes. The inspiral and merger of two compact objects (i.e. bodies whose radius is comparable to their mass, in “geometric” units where G = c = 1) produces copious amounts of gravitational radiation, as was recently discovered by LIGO’s multiple detections of gravitational waves from black hole binary systems.


Alexandre Le Tiec (left) celebrates the detection of gravitational waves and Luc Blanchet (right) thinks about gravitational waves in Quy Nhon, Vietnam

In general relativity, the inspiral and onset of the merger of two compact objects is indeed universal, as it does not depend on the nature of the bodies, be they black holes or neutron stars, or possibly more exotic objects like boson stars or even naked singularities. However, the gravitational waves generated during the post-merger phase depend on the internal structure of the compact objects, and in the case of neutron stars should reveal many details about the scenario for the formation of the final black hole after merger, and the equation of state of nuclear matter deep inside the neutron stars

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Why we built the Holometer

by The Holometer Team: Aaron Chou, Henry Glass, H Richard Gustafson, Craig Hogan, Brittany L Kamai, Ohkyung Kwon, Robert Lanza, Lee McCuller, Stephan S Meyer, Jonathan Richardson, Chris Stoughton, Ray Tomlin and Rainer Weiss.

In a patch of prairie west of Chicago, amidst the rusting relics of 20th century particle beam experiments, we’ve built a new kind of device, designed to monitor positions of isolated, stationary massive bodies—or more precisely, to measure their spacelike correlations in time—with unprecedented fidelity and precision.  Why?


The Holometer Team
Fermi National Accelerator Laboratory: Aaron Chou (Co-PI, project manager), Henry Glass, Craig Hogan (Project Scientist), Chris Stoughton  and Ray Tomlin.          Massachusetts Institute of Technology: Rainer Weiss               University of Chicago: Brittany L.Kamai,Ohkyung Kwon, Robert Lanza, Lee McCuller   Stephan S Meyer (Co-PI) and Jonathan Richardson
University of Michigan: H. Richard Gustafson

The motivation for our experiment starts with a foundational conflict of the two great pillars of physics, relativity and quantum mechanics.  In relativity, space-time is built out of a continuum of events with definite locations in space and time, and it is based on a principle of invariance, that no measurable physical effect can depend on an arbitrary choice of coordinates.  Somehow, that classical world shares dynamical energy and information with quantum mechanical systems built out of a set of states that may be discrete, that are in general indeterminate superpositions of different possibilities not localized in space or time, and that only have physical meaning when correlated, in the context of a specific measurement, with the apparatus of an observer.  Physicists have tried to reconcile these incompatible ideas for a century, starting with famous dialogs between the founding fathers, Einstein and Bohr.

In practice, the conflict has remained theoretical, since it has not led to any problem predicting the results of actual experiments.  But that success is itself a problem: there are no experiments that could give us clues to general principles that may govern a deeper level of reality where a space-time grows out of a quantum system.

Indeed, experiments today solidly confirm both relativity and quantum physics.  Energy transformations of dynamical space-time were spectacularly displayed by the recent detection of gravitational waves from black hole binary inspiral and coalescence.  Delocalized quantum states of particles appear in modern experiments in the form of real-life spooky spacelike correlations that directly challenge Einstein’s notions of reality and locality.


The Fermilab Holometer under construction

Still, no experiment has measured a quantum behavior of space-time itself.  The reason often cited is that the scale where quantum dynamics overwhelms classical space-time, the Planck time, about 10-43 seconds,  lies far beyond the reach of direct metrology.  However, if quantum states are truly delocalized, it may be possible to reach Planck-scale precision in measurements of correlations in space-time position over a macroscopic volume.  The Fermilab Holometer, as we’ve called our machine, is designed to test for such exotic correlations, providing an experimental window into the principles and symmetries of the quantum system that gives rise to space and time.

Theory has provided some important clues that quantum geometry may produce significant exotic correlations in space-time position even on macroscopic scales.  Hints from several directions suggest that the amount of quantum information in a volume of space-time of any size—the number of degrees of freedom—is finite and holographic, given by the area of a two-dimensional bounding surface in Planck units.  The theory of black hole evaporation also suggests that quantum states of geometry are not themselves localized in space and time, but are distributed over a volume as large as the event horizon or curvature radius.

Such results raise the possibility that a laboratory-scale experiment, with enough sensitivity and the right configuration, could measure new spacelike correlations from Planck-scale quantum geometry.  When studying correlations in space-time position, it may not be necessary to resolve a Planck time directly in the time domain.  Instead, extrapolations of standard quantum theory suggest that Planck-scale effects should appear in the “strain noise power spectral density”: a mean square dimensionless strain, or fractional length distortion, per frequency interval.

 The Holometer resembles a scaled-down version of LIGO (see our instrumentation paper in CQG,  It consists of two Michelson interferometers with 40-meter arms, located right next to each other, whose signals are correlated in real time.  The data acquisition system operates fast enough to keep track of positions across the 40-meter device in both space and time.  We’ve shown that we can measure spacelike correlations to a precision of attometers, with a bandwidth of more than 10 MHz—several times faster than the time it takes the laser light to traverse the apparatus.  That sensitivity allows us to measure exotic correlations with strain noise power spectral densities substantially less than a Planck time.

The Holometer Layout

An aerial view showing the layout of both the First and Second-Generation Holometers

Over the course of hundreds of hours, light traverses the apparatus about a trillion times, and the instrument measures self-interference from about 1028 photons, allowing a measurement of strain noise density, limited mainly by quantum statistical noise, about 28 orders of magnitude smaller than the period of the laser light.  So far, measurements are consistent with zero exotic noise from the space-time itself to much better than Planck precision.  This clean null result, reported in, verifies the power of the technique. Along the way, it also places unique constraints on gravitational waves at megahertz frequencies not reachable by LIGO; see

The physical significance of the null result for quantum geometry can be interpreted in terms of models based on symmetries at the Planck scale. Like the famous Michelson-Morley experiment that demonstrated a frame-independent speed of light long before relativity was discovered, it verifies an exact symmetry.  Some day, that symmetry may be understood as a consequence of more fundamental principles of the quantum system that underlies space-time.

The null result has already inspired our next experiment, which will measure a different symmetry at similar sensitivity. During the last year, we have changed the physical layout of the interferometer light paths to include a bend and a transverse segment, so that it can now detect correlated rotational fluctuations.  The reconfigured apparatus will allow us to measure fluctuations in rotation of the local inertial frame that correspond to mean square variations in angular direction per frequency interval less than a Planck time.  Rotational fluctuations of this magnitude, with a specific frequency spectrum (see the calculations in arXiv:1607.03048, arXiv:1509.07997), would be expected if the local inertial frame emerges from a quantum system at the Planck scale.

[1] Chou, A.S., Gustafson, R., Hogan, C., Kamai, B., Kwon, O., Lanza, R., McCuller, L., Meyer, S.S., Richardson, J., Stoughton, C. and Tomlin, R., 2016. First measurements of high frequency cross-spectra from a pair of large Michelson interferometers. Physical Review Letters, 117, p.111102.

[2] Chou, A.S., Gustafson, R., Hogan, C., Kamai, B., Lanza, R., Larson, S.L., McCuller, L., Meyer, S.S., Richardson, J., Stoughton, C. and Tomlin, R., 2016. MHz Gravitational Wave Constraints with Decameter Michelson Interferometers. Physical Review D, 95, 063002.

[3] Hogan, C., Kwon, O. and Richardson, J., 2016. Statistical Model of Exotic Rotational Correlations in Emergent Space-Time. arXiv preprint arXiv:1607.03048. arXiv: 1607.03048

[4] Hogan, C., 2015. Exotic Rotational Correlations in Quantum Geometry. arXiv preprint arXiv:1509.07997. arXiv: 1509.07997

Read the full article in Classical and Quantum Gravity:
The Holometer: an instrument to probe Planckian quantum geometry
Aaron Chou et al. 2017 Class. Quantum Grav. 34 065005

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Can one hear the shape of an ultra compact object?

by Sebastian Völkel and Kostas Kokkotas

A journey from ultra compact objects to quasi-normal modes and back

Never before has gravitational wave research been more promising and attractive than nowadays. With the repeated detection of gravitational waves from binary black hole mergers by LIGO [1–3], not only the long-standing pursue for one of Einstein’s most challenging predictions was confirmed, but also a milestone for many future applications reaching from fundamental physics to astronomy was set. One of the many applications that could follow is addressed in our new CQG paper [4] and shall be broadly presented within a more general introduction to some recent developments in the following lines.

CQG+ format pictures

About the Authors (Left to right): Sebastian Völkel is a first-year PhD student in the Theoretical Astrophysics group of Professor Kostas Kokkotas at the University of Tübingen, located in the south of Germany. Among his research interests is the study of compact objects along with their gravitational wave properties.  Professor Kostas Kokkotas is leading the group of Theoretical Astrophysics at the University of Tübingen. The focus of his research is on the dynamics of compact objects (neutron stars & black-holes), gravitational waves and alternative theories of gravity. More information about the group can be found here.

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