On 14 September 2015, gravitational wave detectors from the LIGO/VIRGO collaboration observed a signal from the coalescence of two black holes with masses of 36 and 29 solar masses at a distance of about 1.3 billion light-years. This extraordinary discovery opens the way in astronomy to study gravitational waves. Huge advances both in fundamental physics astrophysics are expected in the coming years.

*A binary system of two black holes that is very close to the final coalescence. The intense gravitational field distorts the effect of the gravitational deflection of light in the image of stars located in the background. © SXS - Simulating eXtreme Spacetimes*

Researchers at the Paris Astrophysics Institute (IAP, CNRS / UPMC) have been pioneers in the development of new methods for obtaining, from the theory of general relativity, a very accurate prediction for the wave form of the gravitational signal expected during the neutron-star coalescence or black holes. These methods are based on analytical approximations in general relativity, including the development called "post-Newtonian". The templates of post-Newtonian gravitational waves play a crucial role in the process of detecting and analyzing the signal in gravitational wave detectors. Post-Newtonian waveform is valid in the initial phase of spiraling coalescence and connects to numerical calculations for the final merging of two black holes.

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The Paris Astrophysics Institute (IAP, CNRS/UPMC) in English

**Read:**

The full article in the IPA website (CNRS/UPMC) in English

Luc Blanchet, *Gravitational radiation from post-Newtonian sources and inspiralling compact binaries* , *Living Review in Relativity* 17, 2 (2014)

**Watch (in French):**

with an astrophysicienne. Laura Bernard studies the Universe, specifically the modeling of gravitational waves from black holes or spinning neutron stars.

**Notes :**

- A black hole is an object that is so compact that the intensity of its gravitational field prevents matter or radiation from escaping. Such an object can neither emit nor reflect light, so it is black in principle. However this is only true in the classical framework of general relativity: we know from the work of Hawking, a black hole emits radiation due to quantum physical effects; but this radiation is negligible for black holes of large mass, as is the case for GW150914.
- A neutron star is the residue of a massive star that exploded as a supernova, and is composed mainly of neutrons held together by gravity. It is difficult to observe unless it is manifested by a pulsed radio emission (then we say that this is a pulsar) or by the presence of an accretion disk from the uprooting of material a companion star.
- A binary system in astronomy is an assembly of two objects in the Universe bound by gravitational force, and thus are in orbit about their common center of gravity.
- A year after his formulation of the theory of general relativity in November 1915, Einstein predicted the existence of gravitational waves. Then in 1918, he created the famously called "quadrupole" formula that calculates the energy emitted in the form of gravitational waves by a material system. The proof of the existence of gravitational waves (and the validity of the quadrupole formula) was made in 1979 thanks to the observations of the movement of the binary pulsar PSR 1913 + 16, discovered by Hulse and Taylor (Nobel Prize in 1993).

**Images and Illustrations:**

The two graphs below: The gravitational wave observed by the two LIGO detectors of Hanford and Livingstone in a graph showing changes in frequency over time. For a wave, the frequency measures the number of oscillations per second. In the case of a gravitational wave, the signal frequency rises (in the form of "giraffe"), which is characteristic of a coalescence of two compact objects. © Collaboration LIGO/VIRGO

Left: the raw signal observed by the LIGO detector located in Hanford, in a unit 10-21 times the relative change in length of the interferometer arms. Right: the two signals observed at both Hanford and Livingstone sites. The arrival times of the two signals are separated by 7 milliseconds. Blue is shown an adjustment data by a wavelet sum (a mathematical description of the signal, but which is not physical) and in light blue, the best gravitational wave "template" that represents the physical prediction of an outcome based on General Relativity. © Collaboration LIGO/VIRGO

The mass of black holes is measured and compared with theoretical predictions combining analytical and numerical calculations in general relativity. The levels of the curves indicate the probability that we have two simultaneous values of the masses m1 and m2 for two black holes. The curves along each axis show the probability distribution for the mass of each black hole. The peaks of these curves indicate the two most probable values for the event GW150914, or 36 times the mass of the sun for m1 and 29 times the mass for m2, with an uncertainty of about 4 solar masses each. © Collaboration LIGO/VIRGO

Gravitational wave in all three phases of the coalescence of a dual system of compact objects, and the methods used to determine it: The valid calculation post-Newtonian in the spiraling phase is represented by red dots. It connects with the valid numerical calculation in the melting and relaxation phases, which is shown in blue line. DR