## Pulsar Timing Arrays (PTAs)

The timing of an array of ultra-stable pulsars works as a giant galactic detector to observe gravitational waves in the nanoHertz range. Three European consortia (EPTA in Europe, NANOGRAV in North America, PPTA in Australia) have combined their efforts to provide the first constraints on gravitational emission from the population of super-massive binary black holes (between 10^8 and 10^10 solar masses) at the heart of merging galaxies, or from a network of cosmic string loops. For the first time, the obtained limits guide theorists towards new and better gravitational emission scenarios.

The PTA program uses 2300 hours of Nançay Radio Telescope (NRT) time every year. PTAs currently provide the only way of detecting gravitational waves in the nHz to μHz range, and in particular the signature of super massive binary black holes. The NRT provides very high quality data at very high rates.

## Pulsars binaires et tests GR

With orbital periods of a few hours, compact pulsar/white dwarf or pulsar/neutron star binary systems are natural laboratories to test the theories of gravity in the strong field regume. For the most interesting systems, the timing precision achieved with the best radio measurements makes it possible to measure in a few years all the orbital parameters, Keplerian and post-Keplerian. In addition to the precise measurement of the masses of the two components, very useful for all models of the internal structure of neutron stars, one evaluates for these systems: the orbital precession, the parameters of the Shapiro delay, the gravitational redshift, the orbital shrinking caused by the emission of gravitational waves. In some rare cases, we also measure the geodetic precession due to the spin/orbit coupling, we place interesting upper limits on the dipolar gravitational radiation from the coupling between scalar and vector fields (case of very asymmetric binaries), and on the variations of the gravitational constant.

The NRT is one of the few instruments in the world able to provide the quality and the rate of data necessary for this type of application, in particular to sample correctly the orbital phase of these systems. In addition to the PTA data, about 500 telescope hours per year are dedicated specifically to these studies, with the follow-up of 90 binary systems.

## Tests of fundamental physics: gravitation with LISA

The central region of galaxies hosts a Supermassive Black Hole (SMBH). The measurement of the accretion activity of SMHTs gives us information on their population and stellar environment. In particular, the capture of a compact object of 10-100 solar masses (case of an EMRI, for “Extreme Mass Ratio Inspiral”) by a SMNT is detectable thanks to the gravitational waves produced, but only by spatial laser interferometry. The compact object can then be considered as a probe of the TNSM gravitational field, which makes it an ideal source for strong gravity tests. The knowledge of the shape of the gravitational signal, affected by the eigenforce (the whole radiation reaction due to the emission of the waves and the non-radiative contribution due to the ratio of the masses), is imperative for the detection to be carried out, because contrary to binaries of comparable masses, the orbits are extremely complex (strong eccentricity, change of the orbital plane, resonances, zooms and vortices, couplings etc.). The compact object is modeled as a massive particle of infinitesimal size, which allows to neglect its internal structure but introduces the difficulty to regularize the divergences.

In Orléans, we have developed a new strategy for the computation of the emitted waveforms for all types of orbits in the Schwarzschild-Droste geometry and analyzed regularization techniques for the erasure of divergences. We also studied the iterative orbital evolution (the motion of the small mass is continuously corrected by the eigenforce) through the realization of a parallel numerical code (system of second order partial differential equations, by modes – spherical tensor harmonics – in the time domain) and determined the equation of motion and the geodesic deviation. Three other topics of study are: the possibility of detecting the same supermassive black hole binaries before with pulsars and after with LISA in a sequential way, the theorems on entropy and the two-body problem, both Newtonian and Einsteinian, the pedagogy around the equivalence principle and the uniqueness of the falloff in classical physics and in general relativity, the gravitational and Hawking radiation.