A black hole pas de deux

A binary system of black holes merging into a single black hole provides one of the most interesting systems that can be probed by gravitational waves.


One traditionally distinguishes three phases in the phenomenon, often called black hole coalescence. They are depicted in the following diagram, drawn by the renowned black hole specialist, Kip Thorne.

The phases of black hole fusion

The phases of black hole fusion


The two black holes initially form a binary system in rotation. This is mass in motion: it thus loses energy in the form of gravitational waves (the frequency of the gravitational waves is directly related to the frequency of rotation). The two black holes thus get closer and rotate faster. This first phase is called the inspiral phase. The gravitational attraction between the black holes remains small and one can apply standard gravitational methods to compute the gravitational wave signal emitted.


At some point, the two black holes become so close that their horizons touch. The horizon of the black hole is the spherical surface that corresponds to the surface of no return: once crossed, impossible to go backward and tell what we have observed, one is fatally drawn to the centre of the black hole. Once the horizons have touched, one is left with a single black hole. This is the merger phase.


Because gravitational effects close to the horizon are strong, one needs to solve Einstein’s equation in the strong regime. This is done using numerical methods and was a major achievement of the field called numerical relativity in the last ten years (this computation of the form of the gravitational waves during merger was even called the “grand challenge” in the late 1990s). Probing this phase will lead to tests of general relativity in the strong regime (i.e. when gravity is strong), a real premiere.


The final phase is called ringdown. Once the new black hole has been formed, with a rather irregular sort of horizon (made of the two previous horizons), it will shake off its unwanted characteristics through a series of resonant oscillations and emission of gravitational waves. The oscillations are depending on the parameters of the black holes (the initial ones and the final one) and the gravitational waves emitted carry all this information away, encoded in their shape. Again, one will gain precious information on black holes and general relativity by studying the waves produced during ringdown.


The following video shows (credit: NASA/C. Henze) presents a simulation of the merger of two black holes and the resulting emission of gravitational radiation. The coloured fields represent a component of the curvature of space-time. The outer red sheets correspond directly to the outgoing gravitational radiation that may be detected by gravitational-wave observatories.



A final question : how long is a signal of black hole coalescence seen in a detector?


To answer this question, one must realize that detectors function in a given range of frequencies, typically between 10 and 1000 Hz for ground detectors, and between 1/10 000 and 1/10 Hz for space detectors. The gravitational wave signal is seen in the detector only if it falls in this range. But as the two black holes rotate around one another, their rotation frequency increases and thus the frequency of the emitted gravitational waves as well.


The binary system has been evolving for ages but the frequency enters the detector range only a short time before the final plunge (the black holes are then close to one another, the gravitational attraction is stronger and thus the amplitude of the gravitational waves is larger). Typically, ground detectors pick up the signal a few seconds before the merger, and space detectors a few months before.


GW150914: this may not mean anything to you but I can assure you that any gravitational wave physicist is just melting when seeing this codename.


GW150914 is the name of the source observed by the LIGO experiment on 2015, September (09) 14. And, of course GW stands for Gravitational Wave. This is the first source ever discovered by gravitational waves, the first of hopefully a very long series. And their name will follow the same pattern, GW followed by the date of detection.


And what an amazing source: two black holes of respective masses 29 and 36 solar masses which merge into a single one, of 62 solar masses. Add things up: you are missing three solar masses. This corresponds to a release in a few hundredths of second of the corresponding mass-energy in the form of gravitational waves, close to 1050 Watts! This distorts space and time around, and this distortion propagates in all directions…


…1.3 billion years later, exactly on September 14, 2015, at 09:50:45 UTC, this distortion reached Earth and was detected in sequence by the two LIGO detectors, first in Livingston (Louisiana) then in Hanford (Washington state), separated by 7 milliseconds.


Here is the beautiful signal, as shown in the press conference of February 11, and in the article published in Physical Review Letters, and its comparison with the theoretical predictions:

fig1In the top panels, you can see the signals arrived first in Livingston (right), then in Hanford (left): see on the right how well they match! In the medium panel, you find the prediction from relativity for the mass parameters given above. Even with the eye, you see by comparing with the plots above how well observation and prediction match. In the bottom panels, you have the difference between signal and prediction i.e. what we physicists call the noise. Does it seem “noisy” to you? Well, look at the numbers on the vertical axis on the left: the signal is clearly dominating. This is in part because those were massive black holes: the event was a very powerful one.


Note also the horizontal time axis: everything happened in less than half a second. Isn’t that an awfully short time for a cosmic event? Well, you have to remember that the LIGO detector is sensitive to waves in a certain frequency range, basically 10 Hz to a few thousand Hz. The frequency of gravitational waves are directly related to the frequency of rotation of the two black holes. As they get closer over centuries and years, their frequency increases until it is picked up by the detector (when the frequency reaches 10 Hz) but that is only a fraction of a second before the final plunge.


You can see this on the next plot, again provided by the authors of the discovery paper:


You see here the three phases (see post A black hole pas de deux) and to which oscillations in the detector they correspond to. On the bottom panel, you see the evolution with time of the distance between the black hole, in units of the so-called Schwarzschild radius. The Schwarzschild radius is basically the radius of the horizon of the final black hole, approximately 200 km. You also see their relative velocity in units of the velocity of light: it evolves from 1/3 the velocity of light to 2/3 the velocity of light at touchdown! Really an amazing event!


The LIGO collaboration has shown at the press conference the following video showing the collision of these two black holes. Enjoy!

Now, you are ready to get a closer look at the discovery paper. It is written for the scientific community, but the first part is rather accessible. If you have to read only one scientific paper in your lifetime, this may be the one.

And if you are a physics student, with at least some background in classical mechanics, here are a few notes for you to understand better this remarkable event. If you feel dizzy when you see a maths equation, stay away!

Understanding GW150914 notes


Registration to the Gravity! on-line course opens again

The registrations to the course Gravity!  have just reopened on the Futurelearn platform . The first session of this course had attracted 70 000 registered learners last Fall. This new session follows the same programme: it revisits the emergence of the main concepts from Galileo to Newton and Einstein before discussing some of the main aspects of gravity in the Universe -Big Bang, expansion and cosmic inflation, cosmic microwave background, dark matter and dark energy, black holes. And no doubt that gravitational waves will be centre stage on this course!

Classes start on Monday 9 May for six weeks.  You may register here on  the FutureLearn platform. The course is free and registration is open to everyone.

Gravity! is for all those of you curious about the mysteries of the Universe and invites you to understand, without any prerequisite in physics, the foundations of Einstein’s theory that makes gravity “the engine of the Universe”.


Pierre Binétruy and the Gravity! team meet you in the Paris Science Museum

Pierre Binétruy and members of the Gravity! team are in residence at the Palais de la Découverte, the Paris science museum located in the Grand Palais at the bottom of the Champs-Elysées.

This is part of the celebration of the 100th anniversary of General Relativity.

Meet us in person on some of the afternoons of January till March 2016, and perform with us some simple experiments revealing the true nature of gravity. We are located in the entrance rotunda: un chercheur, une manip (“one researcher, one experiment”).



Time 2.30pm-5pm on the following dates:


Wed 6         Antoine Petiteau

Sun 10        Pierre Binétruy

Wed 13       Antoine Petiteau

Sun 17        Pierre Binétruy

Sat 23         Hubert Halloin

Sun 24        Henri Inchauspe

Wed 27        Philippe Bacon

Sat 30         Philippe Bacon


Wed 3          Hubert Halloin

Sat 6           Pierre Binétruy

Sun 7          Pierre Binétruy

Sat 13         Pierre Binétruy

Sun 14        Henri Inchauspe

Wed 17        Pierre Binétruy

Tue 23         Hubert Halloin

Fri 26           Hubert Halloin

Sat 27          Pierre Binétruy

Sun 28         Pierre Binétruy


Sat 5             Henri Inchauspe

Sun 6             Hubert Halloin




Brzmienia/Sonoridades: Gorka Alda celebrates Chillida in Wroclaw

The composer of the music and sounds of Gravity!, Gorka Alda, has conceived two sound installations for the exhibition “Brzmienia/Sonoridades” (Sonorities) dedicated to the sculptures of Eduardo Chillida in Wroclaw, European Capital of Culture 2016.



Gravitación, Eduardo Chillida

The theme of gravitation is recurrent in the work of Eduardo Chillida (1924-2002). Surprisingly, he is using paper for the sculptures on this theme, and the vacuum between the different paper sheets plays a significant role as well.

The exhibition opens this Friday 15  at Awangarda Gallery, in Wroclaw, and continues until March 13 (curators: Inés R. Artola and Ignacio Chillida).

A new particle hint at CERN? Could it tell us something about gravity?

Last December 15, the two experiments which have discovered the Higgs particle at CERN, ATLAS and CMS, have presented the first results of the LHC collider at the highest 13 TeV collision energy and they both announced an excess of 2-photon events at 750 GeV.


This might be the sign of the existence of a new particle with a mass energy of 750 GeV, decaying into two photons like the Higgs. But the evidence is still very preliminary: one only sees small bumps when one plots the number of events versus the energy.


In technical terms, one talks of standard deviations: ATLAS has seen a 3.6 standard deviation, and CMS a 2.6 standard deviation, when the scientific community agrees to talk of a discovery only for standard deviations larger than 5. The excitement comes from the fact that both experiments see an excess at the same mass. But one will probably have to wait another year to accumulate more data and see whether the excess builds up… or disappears if it was just an unhappy coincidence.


But theoretical papers have rushed to provide interpretations of these events. Nature has recently counted almost one hundred papers appearing on the web arXive where the scientific community uploads their papers (108 to this date, see here). Why such an interest? And has it anything to do with gravity?


Well, the Higgs particle discovered in 2012 was the last building block of the Standard Model, which realizes the unification between the electromagnetic and the weak nuclear force. A new particle of mass energy 750 GeV (decaying into two photons) is not accommodated by the Standard Model; it would be a clear sign that this Standard Model has to be revised, or rather enlarged: one would have to go beyond the Standard Model, as we physicists say.


For many of us in the scientific community, this is expected because the Standard Model answers very fundamental questions but leaves many other open. For example, it does not provide a candidate for a dark matter particle. Could the new hypothetical particle be this dark matter particle? Most probably not, but many theoretical papers stress that this first signal of new physics would lead to the discovery of further particles. There is the hope to discover among them this dark matter particle, and thus to solve a puzzle which has been with us since the 1930s (remember that the only signs of dark matter have been so far gravitational, which led some to propose modifications of general relativity to account for the observations).


Another motivation is of a more theoretical nature. The Standard Model only realizes the unification of two fundamental forces (electromagnetic and weak nuclear forces). What about the two others (strong nuclear force and gravitation)? Well, a larger unification requires new dynamics and thus new particles. But the Higgs particle, which provides the masses of all other particles, is very special: its own mass is destabilized by the quantum fluctuations associated with the new particles. In other words, if there is indeed a new particle of mass energy 750 GeV, this would tend to increase the Higgs mass to the same value. But the Higgs mass is measured to be 125 GeV, that is six times smaller. It will then be fascinating to see what protects the Higgs mass from such fluctuations. A new symmetry, for example? In any case, this will give first hand information on the dynamics that may eventually lead to a unification of the microscopic forces with gravity, at a much higher energy. The long sought marriage of quantum physics with general relativity.


2016 thus appears full of promises of major discoveries in fundamental physics. Will it fulfil its promises?


Best wishes to all for this new and exciting year.


Pierre Binétruy

What are MOOC projects for?

Thank you all for the quality of your contributions to the discussion on MOOC funding. Tony asks a central question: what are MOOC projects for? Let me give my own point of view (and my motivation) on this.

It is true that, for the time being, Universities have mostly seen MOOCs as a way of raising their profile and ranking in an increasingly competitive environment. But I believe that we are undergoing a revolution in the way knowledge is disseminated (similar to the printing revolution initiated by Gutenberg) and this revolution means a new role for Universities, or maybe a new type of University.

In parallel, our world has become the global village foreseen by Marshall McLuhan. This struck me last November when the tragic events that took place in my own neighborhood in Paris were immediately known throughout the world and a wave of sympathy almost instantaneously lighted monuments all over the planet in blue, white and red.

In this context, Universities must make their own revolution. For centuries, they were reserved to the happy few, nationals (apart from a few world class universities) with a good curriculum, and in the age range between 18 and 25. Now they should address the whole world, with learners of all ages, diverse origins and cultures, diverse backgrounds and training.

There is clearly a market for that, and some private entities have started investing into this potentially fruitful market. Why should we bother? Because we are dealing with education and training, and thus with our own future as the human race. And because trusting this task only to cost-driven entities will necessarily lead to uniformity and formatting.

Now, you may rightfully think that Universities have also played their roles in formatting people in a certain way. This is why they need to do their own revolution. Why is this necessary? Because, in order to solve the huge problems of our global village, we need a diversity of talents , whether they are to be found in the suburbs of Rio, Capetown or Chongqing, the City of London, the villages of India or Silicon Valley.

But why should Universities get involved in this revolution? That, I understood from MOOC learners. Last spring, we released the French version of Gravity! At the end of the course, we received many thanks and congratulations from the learners. And one message was coming through: “nowadays, we are flooded with information, we have to digest it but no one asks us to think. This is what you did. It may be painful at times, but, in the end, it feels so good!” Now, isn’t that a splendid goal for the University of tomorrow to make people think? And who else could be trusted with such a mission?

Pierre Binétruy

After one week orbiting Earth, heading to L1


Since LISAPathfinder launch, on Thursday December 3rd 2015, teams from the European Space Observations Centre (ESOC) in Darmstadt are working day and night to ensure the orbital operating steps. As illustrated in the figure, these maneuvers consist in correcting the path and increasing by successive pushes the  altitude of the apogee, that is to say, the point on the orbit which is farthest from the Earth . Each time the engine of the propulsion module is activated for several tens of minutes.

Just after the launch the apogee was at an altitude of 1,540km. The first push took place Saturday 07/12/2015 at 5:02 with an increase in speed of 393 m/s which rose the apogee at 3,392km. Then the same day another push at 17:20 rose the apogee at 7.105 km (+ 552 m/s). Then, Tuesday 08/12/2015, two new pushes allowed to reach orbits with apogees at 14,488 km (+ 603 m/s) and then 44,526 km (+ 807 m/s). And the fifth push was operated on 10/12/2015 at 0:34 with an increase in speed of 398 m/s which rose the apogee to 129,122 km.

Finally after running tests on its performance, the engine was activated  on Saturday 12 at 5:18 during 6 minutes to make the final push (+ 234 m/s). This allowed to eject LISAPathfinder outside the Earth’s orbit and to put the satellite on its trajectory towards the Lagrangian point L1. We will have now nearly fifty days to cover the 1.5 million kilometers from the Earth to L1.

Have a good journey LISAPathfinder, arrival late January 2016!

Antoine Petiteau


The difficult issue of MOOC funding

I recently participated to a meeting organized by the French Embassy in London about the future of Massive Open Online Courses (MOOC), from a Franco-British perspective. Many actors in the field were present: platform leaders, university representatives and MOOC designers.


One of the major issues discussed in this meeting was funding. MOOCs are in principle free for learners. But they have a cost. To take the example of Gravity! we have estimated the overall cost, including the hours of all those who have worked on it, to around 100 000€. It may seem huge to you, but this appears to be in the ballpark of the cost of such online courses. And it does not even include the costs of the platform. Of course, most of these costs are covered by scientists providing their own free time to conceive and develop these courses, and to support the learners during the course. But one quarter of the sum concerns the technical aspects of video making and has to be financed with real money. In the case of Gravity! this was mostly supported by Sorbonne Paris Cité, a consortium of Paris Universities which initiated a plan for developing new MOOC projects. But how to sustain the effort in the long run?


Various possibilities were discussed in the London meeting. First of all, platforms are absolutely needed and require funding as well. They often started under the umbrella of a public entity, the Open University for Futurelearn in the UK, or the French Ministry for Higher Education for FUN in France. But they need to acquire some financial autonomy. There are various ways to cover costs, at least partially: some propose to buy the certificate of success (Futurelearn), others offer premium options at a cost (OpenClassrooms). And many look in the direction of corporate courses, funded by private companies for their own purposes, as a complementary source of funding.


But what about the funding of the courses themselves? Obviously universities have an interest in MOOCs: a successful one is great publicity. But their finances are tight and may not follow the development of this type of learning. Platforms return a small fraction of their revenues to the courses but this is far from covering the needs. Obviously, scientists are ready to devote some of their free time. But is it fair to ask young researchers to get involved, without any financial return, when they have to develop their own scientific career? In the case of Gravity! again, the team included around ten postdocs and Ph.D. students who were doing it for the fun of it. But what about course replays?


At Gravity! we have been following a slightly different path. We think that one of the strengths of MOOCs is their availability to everyone, irrespective of their origin, their country, their financial resources, or their level of education. We are thus trying to find donors to support the development of courses. This might not appear to be a priority compared to other good causes, like developing new medical treatments, fighting hunger or supporting children in need. But we believe that learning together about our Universe is the kind of universal activity that brings everyone together, and a way to respect each other, and realize that we are on a small planet that we need to preserve together.


LOGO_RFPU Vb2To be frank, we have not been very successful yet. We have created some years ago with George Smoot an Endowment Fund Physics of the Universe, but we have had difficulties convincing donors that the development of MOOCs is a valuable enough cause to make donations. We have also made a try at crowd-funding, with a platform created by one of our former postdocs. You may have seen in the first page of this website a proposal to fund an extra video for the Gravity! course, but it did not raise much interest: only 96$ since it has been out, and only 4 days still to go!


But we will pursue in this direction and not be discouraged. Certainly online courses will develop as alternatives to teaching as we envisage it now in our Universities. And students might have to pay for them. But we do believe that some other courses, like Gravity! should be aimed at everyone who wants to learn, and to think about the world around us, irrespective of their background, and financial means. So, if you know anybody susceptible to help us, then let them know about us (contact information may be obtained here).


Pierre Binétruy

“Гравитация!” на русском

Gravity! in Russian

Thanks to the dedication and hard work of Mikhail Stolpovskiy, a version of the Gravity! course dubbed in Russian is now available.

Благодаря стараниям Михаила Столповского стал доступен курс “Гравитация!”, продублированный на русском языке.

This will allow all Russian-speaking enthusiasts to get a first contact with the gravitational Universe, and maybe to join later the full course when it is repeated on Futurelearn.

Это позволит русскоязычным слушателям узнать о гравитирующей Вселенной и, возможно, присоединиться позже к полному курсу на платформе Futurelearn.

See below the videos of the first week, where you will follow Galilei, Newton and Einstein to focus on the main concepts of gravity.

Смотрите видео первой недели, где вы проследуете за Галилеем, Ньютоном и Эйнштейном и изучите основные концепции гравитации.

Soon, other videos on PCCPTv on Youtube.

Следите за новыми видео на PCCPTv и Youtube.

Добро пожаловать/Welcome


Галилей и падающие объекты/Galilei and the falling bodies



Первая встреча с относительностью/First encounter with relativity



Ньютон и падающая Луна/Newton and the Moon falling



Эйнштейн в пространстве-времени/Einstein and the space-time



Эйнштейн в падающем лифте/Einstein and the fall of the lift



 Focus: Эксперимент с гравитацией/Experimenting with gravity


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