post-Newtonian Sources Research Articles

Electromagnetic fields in compact binaries: Post-Newtonian wave generation and application to double white dwarfs systems

The aim of this work is twofold: (i) to properly define a wave-generation formalism for compact-supported sources embedded in Einstein-Maxwell theory, relying on matched post-Newtonian and multipolar-post-Minkowskian expansions; (ii) to apply this formalism (which is valid for any type of post-Newtonian sources) to the case of two stars with constant and aligned magnetic dipoles, by computing the fluxes of energy and angular momentum to the next-to-leading order, as well as the gravitational amplitude modes. Assuming eccentric orbits, we derive the evolution of orbital parameters, as well as the observables of the system, notably the gravitational phase for quasicircular orbits. Finally, we give some numerical estimates for the contribution of the magnetic dipoles for some realistic systems. Published by the American Physical Society 2024

Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein–Cartan theory

The generation of gravitational waves from a post-Newtonian source endowed with a quantum spin, modeled by the Weyssenhoff fluid, is investigated in the context of Einstein–Cartan theory at the first post-Newtonian level by resorting to the Blanchet–Damour formalism. After having worked out the basic principles of the hydrodynamics in Einstein–Cartan framework, we study the Weyssenhoff fluid within the post-Newtonian approximation scheme. The complexity of the underlying dynamical equations suggests to employ a discrete description via the point-particle limit, a procedure which permits the analysis of inspiralling spinning compact binaries. We then provide a first application of our results by considering binary neutron star systems.

Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach.

We derive the conservative dynamics of nonspinning binaries to third post-Minkowskian order, using the effective field theory (EFT) approach introduced in [G. Kälin and R. A. Porto, J. High Energy Phys. 11 (2020) 106JHEPFG1029-847910.1007/JHEP11(2020)106] together with the boundary-to-bound dictionary developed in [G. Kälin and R. A. Porto, J. High Energy Phys. 01 (2020) 072JHEPFG1029-847910.1007/JHEP01(2020)072; J. High Energy Phys. 02 (2020) 120.JHEPFG1029-847910.1007/JHEP02(2020)120]. The main ingredient is the scattering angle, which we compute to O(G^{3}) via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated (master) integrals are bootstrapped to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same integrals that appear in the EFT with post-Newtonian sources. For the sake of comparison, we reconstruct the Hamiltonian and the classical limit of the scattering amplitude. Our results are in perfect agreement with those in Bern etal. [Phys. Rev. Lett. 122, 201603 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.201603; J. High Energy Phys. 10 (2019) 206JHEPFG1029-847910.1007/JHEP10(2019)206].

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

To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries — binary star systems composed of neutron stars and/or black holes in their late stage of evolution — require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries — moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

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

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 post-Newtonian 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 effects, 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.

Surface-integral expressions for the multipole moments of post-Newtonian sources and the boosted Schwarzschild solution

New expressions for the multipole moments of an isolated post-Newtonian source, in the form of surface integrals in the outer near-zone, are derived. As an application we compute the ‘source’ quadrupole moment of a Schwarzschild solution boosted to uniform velocity, at the third post-Newtonian (3PN) order. We show that the consideration of this boosted Schwarzschild solution (BSS) is enough to uniquely determine one of the ambiguity parameters in the recent computation of the gravitational wave generation by compact binaries at 3PN order: ζ = −7/33. We argue that this value is the only one for which the Poincaré invariance of the 3PN wave generation formalism is realized. As a check, we confirm the value of ζ by a different method, based on the far-zone expansion of the BSS at fixed retarded time, and a calculation of the relevant nonlinear multipole interactions in the external metric at the 3PN order.

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

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 post-Newtonian 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 effects, 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.