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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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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The silence deep within the universe

by Astrid Eichhorn, Sebastian Mizera and Sumati Surya

Silence is a rare commodity in our everyday, technology-driven lives; from the outright blare of car horns in India, to the quieter, but persistent sounds of mobile phones in Germany, constantly alerting us to the incoming messages, to the 24 hour news cycle on Canadian TV. Finding a few quiet moments, unhindered by the constant onslaught of information requires a considerable effort. Indeed, it often feels that noise, not silence is the generic state of our world.

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Are you going to Loops’ 17?

At the beginning of next week Jennifer Sanders and I will be representing the CQG editorial team at the Loops’ 17 conference at the University of Warsaw in Poland.

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Can boundaries and Hamiltonians get along?

by J. Fernando Barbero G., Benito A. Juárez-Aubry, Juan Margalef-Bentabol and
Eduardo J. S. Villaseñor.

Boundaries are ubiquitous in physics, if anything because most material objects tend to have one… In the context of gravity they play a number of interesting roles: from the definition of conserved quantities in asymptotically flat spacetimes to holography (no lasers here, sorry) or the modeling of black holes. A natural question in the context of the canonical quantization of gravitational theories is how to obtain their Hamiltonian description – in particular the constraints – in the presence of boundaries.


Eduardo and Fernando trying to get inspiration for the new group logo

“Juan, can you hear us?”

“Yes, the connection seems to be working better these days.”

“Hi Benito. Good to see you! Can you also see us?”

“Sorry for the delay, it is early in the morning here. Yeah, I can see you perfectly. Hi, Eduardo and Fernando! Hi, Juan!”

“Hi, there!”

“So, as I told you in my last email, we have to write this CQG+ Insight piece about our traces paper. You know, it should be informative, informal and infused with deep physical insights, so, any suggestions? — Yes, Fernando.”

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Quantum gravity in the sky?

by Abhay Ashtekar and Brajesh Gupt.

Quantum gravity effects in the very early Universe can leave observable imprints.


Abhay Ashtekar (picture taken as a postdoc at Oxford University) is the Eberly Professor of Physics and the Director of the Institute for Gravitation and the Cosmos at the Pennsylvania State University.

The inflationary paradigm traces the genesis of the large-scale structure of the cosmos to astonishingly early times. However, at the onset of inflation spacetime curvature is only about 10-14 times the Planck curvature where quantum gravity effects dominate. Therefore, it is natural to ask if the earlier, pre-inflationary phase of dynamics would change observable predictions of standard inflation. The answer is often assumed to be in the negative. Our CQG paper shows that this conclusion is premature. Specifically, in Loop Quantum Cosmology (LQC) there is an unforeseen interplay between the ultraviolet effects that tame the big bang singularity, and dynamics of infrared modes of cosmological perturbations. As a result, imprints of the quantum spacetime geometry in the Planck regime can manifest themselves at the largest angular scales in the CMB.

In LQC, quantum geometry effects dominate in the Planck regime, replacing the big bang by a quantum bounce, where scalar curvature reaches its finite and universal upper bound. Therefore the radius of curvature has a non-zero lower bound, r_{\rm LQC}. Over the last 7 years, techniques have been developed to describe dynamics of the cosmological perturbations on this quantum background geometry, thereby facing the trans-Planckian issues squarely. Standard inflation assumes Continue reading

Pushing post-Newtonian theory even further!

by Tanguy Marchand, Luc Blanchet and Guillame Faye.

With the spectacular discoveries by the LIGO/VIRGO collaboration of gravitational waves from the coalescence of black-hole binaries, we foresee the possibility of extremely accurate measurements of the so-called post-Newtonian (PN) coefficients that describe the gravitational waveform of these systems in the inspiral phase prior to the final coalescence. The PN coefficients are especially important because they probe the non-linear structure of general relativity (GR) and provide thus very constraining tests of this theory. In turn, they permit accurate measurements of the physical parameters of the binary, essentially the mass of the compact objects and their moment of rotation or spin.

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