post-Newtonian Order Research Articles

Tests of general relativity at the fourth post-Newtonian order

Tests of general relativity at the fourth post-Newtonian order

Test of the Brans–Dicke theory with GW200105 and GW200115

We study whether it is possible to constrain the Brans–Dicke (BD) theory from the measurement of gravitational waves (GW) released in neutron star-black hole collisions. Considering the scalar field modifications through monopole and dipole radiations, we find additional contributions to the phase evolution in the emitted gravitational waveform. After effectively calculating such effect in the post-Newtonian order, we are in a position to measure the scalar field and give bounds on the BD coupling parameter ω BD . We derive the analytical expression for the phase modification due to the orbital eccentricity of eccentric binaries in both general relativity and BD theory. Employing the Bayesian analysis, we obtain the constraints on ω BD from the GW events, GW200105 and GW200115.

Emission signatures from sub-parsec post-Newtonian binaries embedded in circumbinary discs

We studied the dynamical evolution of quasi-circular, equal-mass massive black hole binaries embedded in circumbinary discs from separations of ∼100 Rg down to the merger, following the post merger evolution. The binary orbit evolves owing to the presence of the gaseous disc and the addition of post-Newtonian (PN) corrections up to the 2.5 PN order, therefore including the dissipative gravitational wave back reaction. We investigated two cases of relatively cold and warm circumbinary discs, with aspect ratios of H/R = 0.03, 0.1, respectively, employing 3D hyper-Lagrangian resolution simulations with the GIZMO-MFM code. We extracted spectral energy distributions and light curves in different frequency bands (i.e. X-ray, optical, and UV) from the simulations. We find a clear two orders of magnitude drop in the X-ray flux right before merger if the disc is warm, while we identify a significant increase in the UV flux regardless of the disc temperature. The optical flux shows clear distinctive modulations on the binary orbital period and on the cavity edge period, regardless of the disc temperature. We find that the presence of a cold disc can accelerate the coalescence of the binary by up to 130 s over the last five days of inspiral, implying a phase shift accumulation of about 0.14 radians compared to the binary evolution in vacuum. These differences are triggered by the presence of the gaseous disc and might have implications on the waveforms that can be detected in principle. We discuss the implications that these distinctive signatures might have for existing and upcoming time domain surveys and for multi-messenger astronomy.

Local in Time Conservative Binary Dynamics at Fourth Post-Minkowskian Order.

Leveraging scattering information to describe binary systems in generic orbits requires identifying local and nonlocal in time tail effects. We report here the derivation of the universal (nonspinning) local in time conservative dynamics at fourth post-Minkowskian order, i.e., O(G^{4}). This is achtieved by computing the nonlocal-in-time contribution to the deflection angle, and removing it from the full conservative value in [C. Dlapa et al., Phys. Rev. Lett. 128, 161104 (2022).PRLTAO0031-900710.1103/PhysRevLett.128.161104; C. Dlapa et al., Phys. Rev. Lett. 130, 101401 (2023).PRLTAO0031-900710.1103/PhysRevLett.130.101401]. Unlike the total result, the integration problem involves two scales-velocity and mass ratio-and features multiple polylogarithms, complete elliptic and iterated elliptic integrals, notably in the mass ratio. We reconstruct the local radial action, center-of-mass momentum and Hamiltonian, as well as the exact logarithmic-dependent part(s), all valid for generic orbits. We incorporate the remaining nonlocal terms for ellipticlike motion to sixth post-Newtonian order. The combined Hamiltonian is in perfect agreement in the overlap with the post-Newtonian state of the art. The results presented here provide the most accurate description of gravitationally bound binaries harnessing scattering data to date, readily applicable to waveform modeling.

Post-Newtonian multipoles from the next-to-leading post-Minkowskian gravitational waveform

We consider the frequency-domain leading order and next-to-leading order post-Minkowskian waveforms obtained from the tree-level and one-loop amplitudes describing the scattering of two massive scalar objects and the emission of one graviton. We explicitly calculate their post-Newtonian (PN) limit obtaining an expansion up to the third subleading PN order in all ingredients: the tree-level amplitude, the odd and even parts of the real one-loop kernel, and the Compton or “rescattering” cuts, thus reaching 3PN precision for the latter. We provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the results obtained from the classical multipolar post-Minkowskian method. We find perfect agreement between the two, once the Bondi-Metzner-Sachs supertranslation frame is properly adjusted and the infrared divergences due to rescattering are suitably subtracted in dimensional regularization. This shows that the approach proposed in Georgoudis [An eikonal-inspired approach to the gravitational scattering waveform, 089] can be applied beyond the soft-regime ensuring the agreement between amplitude-based and multipolar post-Minkowskian results for generic frequencies. Published by the American Physical Society 2024

Measuring a Gravitomagnetic Effect with the Triple Pulsar PSR J0337+1715

Measuring a Gravitomagnetic Effect with the Triple Pulsar PSR J0337+1715

Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications

Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications

Accretion flows around spinning compact objects in the post-Newtonian regime

We present the structure of a low angular momentum accretion flows around rotating compact objects incorporating relativistic corrections up to the leading post-Newtonian order. To begin with, we formulate the governing post-Newtonian hydrodynamic equations for the mass and energy-momentum flux without imposing any symmetries. However, for the sake of simplicity, we consider the flow to be stationary, axisymmetric, and inviscid. Toward this, we adapt the polytropic equation of state (EoS) and analyze the vertically integrated accretion flow confined to the equatorial plane. It is shown that the spin-orbit effects manifest themselves in the accretion dynamics. In the present analysis, we focus on global transonic accretion solutions, where a subsonic flow enters far away from the compact object and gradually gains radial velocity as it moves inwards. Thus, the flow becomes supersonic after reaching a certain radius, known as the critical point. To better understand the transonic solutions and examine the effect of post-Newtonian corrections, we classify the post-Newtonian equations into semi-relativistic (SR), semi-Newtonian (SN), and non-relativistic (NR) limits and compare the accretion solutions and their corresponding flow variables. With these, we find that SR and SN flow are in good agreement all throughout, although they deviate largely from the NR ones. Interestingly, the density profile seems to follow the profile ρ ∝ r -3/2 in the post-Newtonian regime. The present study has the potential to connect Newtonian and GR descriptions of accretion dynamics.

Binary dynamics to second post-Newtonian order in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity from effective field theory

Binary dynamics to second post-Newtonian order in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity from effective field theory

Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: Exploring spin-gauge flexibility

Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: Exploring spin-gauge flexibility

Impact of Overlapping Signals on Parameterized Post-Newtonian Coefficients in Tests of Gravity

Gravitational waves have been instrumental in providing deep insights into the nature of gravity. Next-generation detectors, such as the Einstein Telescope, are predicted to have a higher detection rate given the increased sensitivity and lower cutoff frequency. However, this increased sensitivity raises challenges concerning parameter estimation due to the foreseeable overlap of signals from multiple sources. Overlapping signals (OSs), if not properly identified, may introduce biases in estimating post-Newtonian (PN) coefficients in parameterized tests of general relativity (GR). We investigate how OSs affect −1PN to 2PN terms in parameterized GR tests, examining their potential to falsely suggest GR deviations. We estimate the prevalence of such misleading signals in next-generation detectors, and their collective influence on GR tests. We compare the effects of OSs on coefficients at different PN orders, concluding that overall the 1PN coefficient suffers the most. Our findings also reveal that while a nonnegligible portion of OSs exhibit biases in PN coefficients that might individually prefer to conclude deviations from GR, collectively, the direction to deviate is random and a statistical combination will still be in favor of GR.

Revisiting the gravitomagnetic clock effect

To the first post-Newtonian order, if two test particles revolve in opposite directions about a massive, spinning body along two circular and equatorial orbits with the same radius, they take different times to return to the reference direction relative to which their motion is measured: it is the so-called gravitomagnetic clock effect. The satellite moving in the same sense of the rotation of the primary is slower, and experiences a retardation with respect to the case when the latter does not spin, while the one circling in the opposite sense of the rotation of the source is faster, and its orbital period is shorter than it would be in the static case. The resulting time difference due to the stationary gravitomagnetic field of the central spinning body is proportional to the angular momentum per unit mass of the latter through a numerical factor which so far has been found to be 4π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\\pi $$\\end{document}. A numerical integration of the equations of motion of a fictitious test particle moving along a circular path lying in the equatorial plane of a hypothetical rotating object by including the gravitomagnetic acceleration to the first post-Newtonian order shows that, actually, the gravitomagnetic corrections to the orbital periods are larger by a factor of 4 in both the prograde and retrograde cases. Such an outcome, which makes the proportionality coefficient of the gravitomagnetic difference in the orbital periods of the two counter-revolving orbiters equal to 16π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$16\\pi $$\\end{document}, confirms an analytical calculation recently published in the literature by the present author. It is an important result in view of the astrophysical implications of the gravitomagnetic clock effect around Kerr black holes.

Renormalizing Love: tidal effects at the third post-Newtonian order

We present the conservative effective two-body Hamiltonian at the third order in the post-Newtonian expansion with gravitoelectric quadrupolar dynamical tidal-interactions. Our derivation of the effective two-body Lagrangian is based on the diagrammatic effective field theory approach and it involves Feynman integrals up to three loops, which are evaluated within the dimensional regularization scheme. The elimination of the divergent terms occurring in the effective Lagrangian requires the addition of counterterms to ensure finite observables, thereby introducing a renormalization group flow to the post-adiabatic Love number. As a limiting case of the renormalized dynamical effective Hamiltonian, we also derive the effective Hamiltonian for adiabatic tides, and, in this regime, calculate the binding energy for a circular orbit, and the scattering angle in a hyperbolic scattering.

Radiative losses and radiation-reaction effects at the first post-Newtonian order in Einstein–Cartan theory

Gravitational radiation-reaction phenomena occurring in the dynamics of inspiralling compact binary systems are investigated at the first post-Newtonian order beyond the quadrupole approximation in the context of Einstein–Cartan theory, where quantum spin effects are modeled via the Weyssenhoff fluid. We exploit balance equations for the energy and angular momentum to determine the binary orbital decay until the two bodies collide. Our framework deals with both quasi-elliptic and quasi-circular trajectories, which are then smoothly connected. Key observables like the laws of variation of the orbital phase and frequency characterizing the quasi-circular motion are derived analytically. We conclude our analysis with an estimation of the spin contributions at the merger, which are examined both in the time domain and the Fourier frequency space through the stationary wave approximation.

Tidal effects up to next-to-next-to-leading post-Newtonian order in massless scalar-tensor theories

Tidal effects up to next-to-next-to-leading post-Newtonian order in massless scalar-tensor theories

Spacetime symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

Spacetime symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order

Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order

Compact binary systems in Einstein-Æther gravity: Direct integration of the relaxed field equations to 2.5 post-Newtonian order

Compact binary systems in Einstein-Æther gravity: Direct integration of the relaxed field equations to 2.5 post-Newtonian order

The third post-Newtonian equatorial motion in Kerr spacetime

We calculate the third post-Newtonian (PN) order solution for the equatorial motion of a test particle in Kerr spacetime. In particular, we obtain the effects of the spin-induced quadrupole on the periastron advance and the orbital period at the 3PN order.

Poincaré invariance of spinning binary dynamics in the post-Minkowskian Hamiltonian approach

Abstract We initiate the construction of the global Poincaré algebra generators in the context of the post-Minkowskian Hamiltonian formulation of gravitating binary dynamics in isotropic coordinates that is partly inspired by scattering amplitudes. At the first post-Minkowskian order, we write down the Hamiltonian in a form valid in an arbitrary inertial frame. Then we construct the boost generator at the same order which uniquely solves all the equations required by the Poincaré algebra. Our results are linear in Newton’s constant but exact in velocities and spins, including all spin-multipole moments. We also construct explicitly the canonical transformations that prove the equivalence between our new generators and the corresponding generators in the ADM coordinates up to the second post-Newtonian order.