Parametric derivation of the observable relativistic periastron advance for binary pulsars

We compute the dimensionless relativistic periastron advance parameter $k$, which is measurable from the timing of relativistic binary pulsars. We employ for the computation the recently derived Keplerian-type parametric solution to the post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The parametric solution and hence the parameter $k$ are applicable for the cases of \emph{simple precession}, namely, case (i), the binary consists of equal mass compact objects, having two arbitrary spins, and case (ii), the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. Our expression, for the cases considered, is in agreement with a more general formula for the 2PN accurate $k$, relevant for the relativistic double pulsar PSR J0737--3039, derived by Damour and Sch\"afer many years ago, using a different procedure.Comment: 12 pages including 1 figure; submitted to PR

Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction

We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser, and Misner-type coordinates. Our parametric solution is applicable in the following two distinct cases: (i) the binary consists of equal mass compact objects, having two arbitrary spins, and (ii) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. As an application of our parametrization, we present gravitational wave polarizations, whose amplitudes are restricted to the leading quadrupolar order, suitable to describe gravitational radiation from spinning compact binaries moving in eccentric orbits. The present parametrization will be required to construct `ready to use' reference templates for gravitational waves from spinning compact binaries in inspiralling eccentric orbits. Our parametric solution for the post-Newtonian accurate conservative dynamics of spinning compact binaries clearly indicates, for the cases considered, the absence of chaos in these systems. Finally, we note that our parametrization provides the first step in deriving a fully second post-Newtonian accurate `timing formula', that may be useful for the radio observations of relativistic binary pulsars like J0737-3039.Comment: 18 pages, accepted by Phys. Rev.

Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order

We obtain an efficient description for the dynamics of nonspinning compact binaries moving in inspiralling eccentric orbits to implement the phasing of gravitational waves from such binaries at the 3.5 post-Newtonian (PN) order. Our computation heavily depends on the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D \textbf{70}, 064028 (2004)], and the 3PN accurate generalized quasi-Keplerian parametric solution to the conservative dynamics of nonspinning compact binaries moving in eccentric orbits, available in [R.-M. Memmesheimer, A. Gopakumar, and G. Sch\"afer, Phys. Rev. D \textbf{70}, 104011 (2004)]. The gravitational-wave (GW) polarizations $h_{+}$ and $h_{\times}$ with 3.5PN accurate phasing should be useful for the earth-based GW interferometers, current and advanced, if they plan to search for gravitational waves from inspiralling eccentric binaries. Our results will be required to do \emph{astrophysics} with the proposed space-based GW interferometers like LISA, BBO, and DECIGO.Comment: 22 pages including 2 figures; submitted to PR

Phasing of gravitational waves from inspiralling eccentric binaries

We provide a method for analytically constructing high-accuracy templates for the gravitational wave signals emitted by compact binaries moving in inspiralling eccentric orbits. By contrast to the simpler problem of modeling the gravitational wave signals emitted by inspiralling {\it circular} orbits, which contain only two different time scales, namely those associated with the orbital motion and the radiation reaction, the case of {\it inspiralling eccentric} orbits involves {\it three different time scales}: orbital period, periastron precession and radiation-reaction time scales. By using an improved `method of variation of constants', we show how to combine these three time scales, without making the usual approximation of treating the radiative time scale as an adiabatic process. We explicitly implement our method at the 2.5PN post-Newtonian accuracy. Our final results can be viewed as computing new `post-adiabatic' short period contributions to the orbital phasing, or equivalently, new short-period contributions to the gravitational wave polarizations, $h_{+,\times}$, that should be explicitly added to the `post-Newtonian' expansion for $h_{+,\times}$, if one treats radiative effects on the orbital phasing of the latter in the usual adiabatic approximation. Our results should be of importance both for the LIGO/VIRGO/GEO network of ground based interferometric gravitational wave detectors (especially if Kozai oscillations turn out to be significant in globular cluster triplets), and for the future space-based interferometer LISA.Comment: 49 pages, 6 figures, high quality figures upon reques

Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits

We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are explicitly given in terms of the 3PN accurate conserved orbital energy and angular momentum in both Arnowitt, Deser, and Misner-type and harmonic coordinates. Our representation will be required to construct post-Newtonian accurate `ready to use' search templates for the detection of gravitational waves from compact binaries in inspiralling eccentric orbits. Due to the presence of certain 3PN accurate gauge invariant orbital elements, the parametrization should be useful to analyze the compatibility of general relativistic numerical simulations involving compact binaries with the corresponding post-Newtonian descriptions. If required, the present parametrization will also be needed to compute post-Newtonian corrections to the currently employed `timing formula' for the radio observations of relativistic binary pulsars.Comment: 33 pages, 1 figur

Testing gravity to second post-Newtonian order: a field-theory approach

A new, field-theory-based framework for discussing and interpreting tests of gravity, notably at the second post-Newtonian (2PN) level, is introduced. Contrary to previous frameworks which attempted at parametrizing any conceivable deviation from general relativity, we focus on the best motivated class of models, in which gravity is mediated by a tensor field together with one or several scalar fields. The 2PN approximation of these "tensor-multi-scalar" theories is obtained thanks to a diagrammatic expansion which allows us to compute the Lagrangian describing the motion of N bodies. In contrast with previous studies which had to introduce many phenomenological parameters, we find that the 2PN deviations from general relativity can be fully described by only two new 2PN parameters, epsilon and zeta, beyond the usual (Eddington) 1PN parameters beta and gamma. It follows from the basic tenets of field theory, notably the absence of negative-energy excitations, that (beta-1), epsilon and zeta (as well as any new parameter entering higher post-Newtonian orders) must tend to zero with (gamma-1). It is also found that epsilon and zeta do not enter the 2PN equations of motion of light. Therefore, light-deflection or time-delay experiments cannot probe any theoretically motivated 2PN deviation from general relativity, but they can give a clean access to (gamma-1), which is of greatest significance as it measures the basic coupling strength of matter to the scalar fields. Because of the importance of self-gravity effects in neutron stars, binary-pulsar experiments are found to constitute a unique testing ground for the 2PN structure of gravity. A simplified analysis of four binary pulsars already leads to significant constraints: |epsilon| < 7x10^-2, |zeta| < 6x10^-3.Comment: 63 pages, 11 figures.ps.tar.gz.uu, REVTeX 3.

Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order

Gravitational waves generated by inspiralling compact binaries are investigated to the second--post-Newtonian (2PN) approximation of general relativity. Using a recently developed 2PN-accurate wave generation formalism, we compute the gravitational waveform and associated energy loss rate from a binary system of point-masses moving on a quasi-circular orbit. The crucial new input is our computation of the 2PN-accurate ``source'' quadrupole moment of the binary. Tails in both the waveform and energy loss rate at infinity are explicitly computed. Gravitational radiation reaction effects on the orbital frequency and phase of the binary are deduced from the energy loss. In the limiting case of a very small mass ratio between the two bodies we recover the results obtained by black hole perturbation methods. We find that finite mass ratio effects are very significant as they increase the 2PN contribution to the phase by up to 52\%. The results of this paper should be of use when deciphering the signals observed by the future LIGO/VIRGO network of gravitational-wave detectors.Comment: 43 pages, LaTeX-ReVTeX, no figures

Theoretical Aspects of the Equivalence Principle

We review several theoretical aspects of the Equivalence Principle (EP). We emphasize the unsatisfactory fact that the EP maintains the absolute character of the coupling constants of physics while General Relativity, and its generalizations (Kaluza-Klein,..., String Theory), suggest that all absolute structures should be replaced by dynamical entities. We discuss the EP-violation phenomenology of dilaton-like models, which is likely to be dominated by the linear superposition of two effects: a signal proportional to the nuclear Coulomb energy, related to the variation of the fine-structure constant, and a signal proportional to the surface nuclear binding energy, related to the variation of the light quark masses. We recall the various theoretical arguments (including a recently proposed anthropic argument) suggesting that the EP be violated at a small, but not unmeasurably small level. This motivates the need for improved tests of the EP. These tests are probing new territories in physics that are related to deep, and mysterious, issues in fundamental physics.Comment: 21 pages, no figures; submitted to a "focus issue" of Classical and Quantum Gravity on Tests of the Weak Equivalence Principle, organized by Clive Speake and Clifford Wil

Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms

A Lagrangian from which derive the third post-Newtonian (3PN) equations of motion of compact binaries (neglecting the radiation reaction damping) is obtained. The 3PN equations of motion were computed previously by Blanchet and Faye in harmonic coordinates. The Lagrangian depends on the harmonic-coordinate positions, velocities and accelerations of the two bodies. At the 3PN order, the appearance of one undetermined physical parameter \lambda reflects an incompleteness of the point-mass regularization used when deriving the equations of motion. In addition the Lagrangian involves two unphysical (gauge-dependent) constants r'_1 and r'_2 parametrizing some logarithmic terms. The expressions of the ten Noetherian conserved quantities, associated with the invariance of the Lagrangian under the Poincar\'e group, are computed. By performing an infinitesimal ``contact'' transformation of the motion, we prove that the 3PN harmonic-coordinate Lagrangian is physically equivalent to the 3PN Arnowitt-Deser-Misner Hamiltonian obtained recently by Damour, Jaranowski and Sch\"afer.Comment: 30 pages, to appear in Classical and Quantum Gravit