The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

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Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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Testing general relativity with present and future astrophysical observations

The double pulsar system PSR J0737-3039A/B is unique in that both neutron stars are detectable as radio pulsars. They are also known to have much higher mean orbital velocities and accelerations than those of other binary pulsars. The system is therefore a good candidate for testing Einstein's theory of general relativity and alternative theories of gravity in the strong-field regime. We report on precision timing observations taken over the 2.5 years since its discovery and present four independent strong-field tests of general relativity. These tests use the theory-independent mass ratio of the two stars. By measuring relativistic corrections to the Keplerian description of the orbital motion, we find that the “post-Keplerian” parameter s agrees with the value predicted by general relativity within an uncertainty of 0.05%, the most precise test yet obtained. We also show that the transverse velocity of the system's center of mass is extremely small. Combined with the system's location near the Sun, this result suggests that future tests of gravitational theories with the double pulsar will supersede the best current solar system tests. It also implies that the second-born pulsar may not have formed through the core collapse of a helium star, as is usually assumed.

https://arxiv.org/pdf/astro-ph/0609417.pdf

Tests of General Relativity from Timing the Double Pulsar

The clocklike properties of pulsars moving in the gravitational fields of their unseen neutron-star companions have allowed unique tests of general relativity and provided evidence for gravitational radiation. We report here the detection of the 2.8-second pulsar J07373039B as the companion to the 23-millisecond pulsar J07373039A in a highly relativistic double neutron star system, allowing unprecedented tests of fundamental gravitational physics. We observed a short eclipse of J07373039A by J07373039B and orbital modulation of the flux density and the pulse shape of J07373039B, probably because of the influence of J07373039A’s energy flux on its magnetosphere. These effects will allow us to probe magneto-ionic properties of a pulsar magnetosphere. Double neutron star (DNS) binaries are rare, and only six such systems are known. How

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A double-pulsar system: A rare laboratory for relativistic gravity and plasma physics

We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar population to over 1800. There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy, and a further 140 pulsars in 26 of the Galactic globular clusters. Recent highlights include the discovery of the young relativistic binary system PSR J1906+0746, a rejuvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of 1.5M , a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric (e = 0.44) orbit around an unevolved companion.

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Binary and Millisecond Pulsars

The contributions to the periastron advance of a system of two condensed bodies coming from relativistic dynamical effects of order higher than the usual first post-Newtonian (1PN) equations of motion are investigated. The structure of the solution of the orbital second post-Newtonian (2PN) equations of motion is given in a simple parametrized form. The contributions to the secular periastron advance, and to the period, of orbital 2PN effects are then explicitly worked out by using the Hamilton-Jacobi method. The spin-orbit contribution to the secular precession of the orbit in space is rederived in a streamlined way by making full use of Hamiltonian methods. These results are then applied to the theoretical interpretation of the observational data of pulsars in close eccentric binary systems. It is shown that the higher-order relativistic contributions are already of theoretical and astrophysical significance for interpreting the high-precision measurement of the secular periastron advance of PSR 1913+16 achieved by Taylor and coworkers. The case of extremely fast spinning (millisecond) binary pulsars is also discussed, and shown to offer an easier ground for getting new tests of general relativity, and/or, a direct measurement of the moment of inertia of a neutron star.

G. Schäeer

Papers

Higher Order Relativistic Periastron Advances and Binary Pulsars