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Register a new userPost-Newtonian Approximations, Compact Binaries, and Strong-Field Tests of Gravity
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This is an extended summary of the two parallel sessions held at MG11: PPN1 ``Strong Gravity and Binaries (chaired by L.B. and L.G.) and PPN2 ``Post-Newtonian Dynamics in Binary Objects (chaired by G.S.). The aims and contents of these sessions were close to each other and overlapping. It is natural to review both sessions in one joint contribution to the MG11 Proceedings. The summary places the delivered talks in a broader perspective of current studies in this area. One can find more details in individual contributions of the respective authors.
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General relativity is a fully conservative theory, but there exist other possible metric theories of gravity. We consider non-conservative ones with a parameterized post-Newtonian (PPN) parameter, $zeta_2$. A non-zero $zeta_2$ induces a self-acceleration for the center of mass of an eccentric binary pulsar system, which contributes to the second time derivative of the pulsar spin frequency, $ddot{ u}$. In our work, using the method in Will (1992), we provide an improved analysis with four well-timed, carefully-chosen binary pulsars. In addition, we extend Wills method and derive $zeta_2$s effect on the third time derivative of the spin frequency, $dddot{ u}$. For PSR B1913+16, the constraint from $dddot{ u}$ is even tighter than that from $ddot{ u}$. We combine multiple pulsars with Bayesian inference, and obtain an upper limit, $left|zeta_{2}right|<1.3times10^{-5}$ at 95% confidence level, assuming a flat prior in $log_{10} left| zeta_{2}right|$. It improves the existing bound by a factor of three. Moreover, we propose an analytical timing formalism for $zeta_2$. Our simulated times of arrival with simplified assumptions show binary pulsars capability in limiting $zeta_{2}$, and useful clues are extracted for real data analysis in future. In particular, we discover that for PSRs B1913+16 and J0737$-$3039A, $dddot{ u}$ can yield more constraining limits than $ddot{ u}$.
There are theoretical frameworks, such as the large extra dimension models, which predict the strengthening of the gravitational field in short distances. Here we obtain new empiric constraints for deviations of standard gravity in the atomic length scale from analyses of recent and accurate data of hydrogen spectroscopy. The new bounds, extracted from 1S-3S transition, are compared with previous limits given by antiprotonic Helium spectroscopy. Independent constraints are also determined by investigating the effects of gravitational spin-orbit coupling on the atomic spectrum. We show that the analysis of the influence of that interaction, which is responsible for the spin precession phenomena, on the fine structure of the states can be employed as a test of a post-Newtonian potential in the atomic domain. The constraints obtained here from 2P_{1/2}-2P_{3/2} transition in hydrogen are tighter than previous bounds determined from measurements of the spin precession in an electron-nucleus scattering.
We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second Post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second Post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.
The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasicircular, inspiralling binaries, the Christodoulou memory produces a growing, nonoscillatory change in the gravitational-wave plus polarization, resulting in the permanent displacement of a pair of freely-falling test masses after the wave has passed. In addition to its nonoscillatory behavior, the Christodoulou memory is interesting because even though it originates from 2.5 post-Newtonian (PN) order multipole interactions, it affects the waveform at leading (Newtonian/quadrupole) order. The memory is also potentially detectable in binary black-hole mergers. While the oscillatory pieces of the gravitational-wave polarizations for quasicircular, inspiralling compact binaries have been computed to 3PN order, the memory contribution to the polarizations has only been calculated to leading order (the next-to-leading order 0.5PN term has previously been shown to vanish). Here the calculation of the memory for quasicircular, inspiralling binaries is extended to 3PN order. While the angular dependence of the memory remains qualitatively unchanged, the PN correction terms tend to reduce the memorys magnitude. Explicit expressions are given for the memory contributions to the plus polarization and the spin-weighted spherical-harmonic modes of the metric and curvature perturbations. Combined with the recent results of Blanchet et al.(2008), this completes the waveform to 3PN order. This paper also discusses: (i) the difficulties in extracting the memory from numerical simulations, (ii) other nonoscillatory effects that enter the waveform at high PN orders, and (iii) issues concerning the observability of the memory.
We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasi-circular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparisons with numerical-relativity simulations.
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