Search

We present a scattering amplitude formalism to study the tidal heating effects of nonspinning neutron stars incorporating both worldline effective field theory and relativistic stellar perturbation theory. In neutron stars, tidal heating arises from fluid viscosity due to various scattering processes in the interior. It also serves as a channel for the exchange of energy and angular momentum between the neutron star and its environment. In the interior of the neutron star, we first derive two master perturbation equations that capture fluid perturbations accurate to linear order in frequency. Remarkably, these equations receive no contribution from bulk viscosity due to a peculiar adiabatic incompressibility which arises in stellar fluid for non-barotropic perturbations. In the exterior, the metric perturbations reduce to the Regge-Wheeler (RW) equation which we solve using the analytical Mano-Suzuki-Takasugi (MST) method. We compute the amplitude for gravitational waves scattering off a neutron star, also known as gravitational Raman scattering. From the amplitude, we obtain expressions for the electric quadrupolar static Love number and the leading dissipation number to all orders in compactness. We then compute the leading dissipation number for various realistic equation-of-state(s) and estimate the change in the number of gravitational wave cycles due to tidal heating during inspiral in the LIGO-Virgo-KAGRA (LVK) band., Comment: 28 pages, 2 tables, 1 appendix, version 2

On 29 May 2023, the LIGO Livingston observatory detected the gravitational-wave signal GW230529_181500 from the merger of a neutron star with a lower mass-gap compact object. Its long inspiral signal provides a unique opportunity to test General Relativity (GR) in a parameter space previously unexplored by strong-field tests. In this work, we performed parameterized inspiral tests of GR with GW230529_181500. Specifically, we search for deviations in the frequency-domain GW phase by allowing for agnostic corrections to the post-Newtonian coefficients. We performed tests with the Flexible Theory Independent (FTI) and Test Infrastructure for General Relativity (TIGER) frameworks using several quasi-circular waveform models that capture different physical effects (higher modes, spins, tides). We find that the signal is consistent with GR for all deviation parameters. Assuming the primary object is a black hole, we obtain particularly tight constraints on the dipole radiation at $-1$PN order of $|\delta\hat{\varphi}_{-2}| \lesssim 8 \times 10^{-5}$, which is a factor $\sim17$ times more stringent than previous bounds from the neutron star--black hole merger GW200115_042309, as well as on the 0.5PN and 1PN deviation parameters. We discuss some challenges that arise when analyzing this signal, namely biases due to correlations with tidal effects and the degeneracy between the 0PN deviation parameter and the chirp mass. To illustrate the importance of GW230529_181500 for tests of GR, we mapped the agnostic $-1$PN results to a class of Einstein-scalar-Gauss-Bonnet (ESGB) theories of gravity. We also conducted an analysis probing the specific phase deviation expected in ESGB theory and obtain an upper bound on the Gauss-Bonnet coupling of $\ell_{\rm GB} \lesssim 0.51~\rm{M}_\odot$ ($\sqrt{\alpha_{\rm GB}} \lesssim 0.28$ km), which is better than any previously reported constraint., Comment: 19 pages, 9 figures

The response of black holes to small perturbations is known to be partially described by a superposition of quasinormal modes. Despite their importance to enable strong-field tests of gravity, little to nothing is known about what overtones and quasinormal-mode amplitudes are like for black holes in extensions to general relativity. We take a first step in this direction and study what is arguably the simplest model that allows first-principle calculations to be made: a nonrotating black hole in an effective-field-theory extension of general relativity with cubic-in-curvature terms. Using a phase-amplitude scheme that uses analytical continuation and the Pr\"ufer transformation, we compute, for the first time, the quasinormal overtone frequencies (in this theory) and quasinormal-mode excitation factors (in any theory beyond general relativity). We find that the overtone quasinormal frequencies and their excitation factors are more sensitive than the fundamental mode to the lengthscale $l$ introduced by the higher-derivative terms in the effective field theory. We argue that a description of all overtones cannot be made within the regime of validity of the effective field theory, and we conjecture that this is a general feature of any extension to general relativity that introduces a new lengthscale. We also find that a parametrization of the modifications to the general-relativistic quasinormal frequencies in terms of the ratio between $l$ and the black hole's mass is somewhat inadequate, and we propose a better alternative. As an application, we perform a preliminary study of the implications of the breakdown, in the effective field theory, of the equivalence between the quasinormal mode spectra associated to metric perturbations of polar and axial parity of the Schwarzschild black hole in general relativity. We also present a simple justification for the loss of isospectrality., Comment: 21 pages, 9 figures, 1 table. (v2) Matches version published in Phys. Rev. D

For the analysis of gravitational-wave signals, fast and accurate gravitational-waveform models are required. These enable us to obtain information on the system properties from compact binary mergers. In this article, we introduce the NRTidalv3 model, which contains a closed-form expression that describes tidal effects, focusing on the description of binary neutron star systems. The model improves upon previous versions by employing a larger set of numerical-relativity data for its calibration, by including high-mass ratio systems covering also a wider range of equations of state. It also takes into account dynamical tidal effects and the known post-Newtonian mass-ratio dependence of individual calibration parameters. We implemented the model in the publicly available LALSuite software library by augmenting different binary black hole waveform models (IMRPhenomD, IMRPhenomX, and SEOBNRv5_ROM). We test the validity of NRTidalv3 by comparing it with numerical-relativity waveforms, as well as other tidal models. Finally, we perform parameter estimation for GW170817 and GW190425 with the new tidal approximant and find overall consistent results with respect to previous studies.

A major science goal of gravitational-wave (GW) observations is to probe the nature of gravity and constrain modifications to General Relativity. An established class of modified gravity theories are scalar-tensor models, which introduce an extra scalar degree of freedom. This affects the internal structure of neutron stars (NSs), as well as their dynamics and GWs in binary systems, where distinct novel features can arise from the appearance of scalar condensates in parts of the parameter space. To improve the robustness of the analyses of such GW events requires advances in modeling internal-structure-dependent phenomena in scalar-tensor theories. We develop an effective description of potentially scalarized NSs on large scales, where information about the interior is encoded in characteristic Love numbers or equivalently tidal deformabilities. We demonstrate that three independent tidal deformabilities are needed to characterize the configurations: a scalar, tensor, and a novel 'mixed' parameter, and develop the general methodology to compute these quantities. We also present case studies for different NS equations of state and scalar properties and provide the mapping between the deformabilities in different frames often used for calculations. Our results have direct applications for future GW tests of gravity and studies of potential degeneracies with other uncertain physics such as the equation of state or presence of dark matter in NS binary systems., Comment: v2, 44 pages, 29 figures. Discussion, references and plots added

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., Comment: 27 pages, 3 figures, 1 table; matches the published version. arXiv admin note: text overlap with arXiv:2304.02030

We present a gravitoelectric quadrupolar dynamical tidal-interaction Hamiltonian for a compact binary system, that is valid to second order in the post-Newtonian expansion. Our derivation uses the diagrammatic effective field theory approach, and involves Feynman integrals up to two loops, evaluated with the dimensional regularization scheme. We also derive the effective Hamiltonian for adiabatic tides, obtained by taking the appropriate limit of the dynamical effective Hamiltonian, and we check its validity by verifying the complete Poincar\'e algebra. In the adiabatic limit, we also calculate two gauge-invariant observables, namely, the binding energy for a circular orbit and the scattering angle in a hyperbolic scattering. Our results are important for developing accurate gravitational waveform models for neutron-star binaries for present and future gravitational-wave observatories., Comment: 20 pages, 2 figures, 1 table; matches the published version

Universal relations that are insensitive to the equation of state (EoS) are useful in reducing the parameter space when measuring global quantities of neutron stars (NSs). In this paper, we reveal a new universal relation that connects the eccentricity to the radius and moment of inertia of rotating NSs. We demonstrate that the universality of this relation holds for both conventional NSs and bare quark stars (QSs) in the slow rotation approximation, albeit with different relations. The maximum relative deviation is approximately $1\%$ for conventional NSs and $0.1\%$ for QSs. Additionally, we show that the universality still exists for fast-rotating NSs if we use the dimensionless spin to characterize their rotation. The new universal relation will be a valuable tool to reduce the number of parameters used to describe the shape and multipoles of rotating NSs, and it may also be used to infer the eccentricity or moment of inertia of NSs in future X-ray observations., Comment: 7 pages, 5 figures; accepted by ApJ

Gravitational waves (GWs) from binary neutron stars (NSs) have opened unique opportunities to constrain the nuclear equation of state by measuring tidal effects associated with the excitation of characteristic modes of the NSs. This includes gravitomagnetic modes associated with the Coriolis effect, whose frequencies are proportional to the NS's spin frequency, and for which the spin orientation determines the subclass of modes that are predominantly excited. We advance the GW models for these effects that are needed for data analysis by first developing a description for the adiabatic signatures from gravitomagnetic modes in slowly rotating NSs. We show that they can be encapsulated in an effective Love number which differs before and after a mode resonance. Combining this with a known generic model for abrupt changes in the GWs at the mode resonance and a point-mass baseline leads to an efficient description which we use to perform case studies of the impacts of gravitomagnetic effects for measurements with Cosmic Explorer, an envisioned next-generation GW detector. We quantify the extent to which neglecting (including) the effect of gravitomagnetic modes induces biases (significantly reduces statistical errors) in the measured tidal deformability parameters, which depend on the equation of state. Our results substantiate the importance of dynamical gravitomagnetic tidal effects for measurements with third generation detectors., Comment: 20 pages, 14 figures

The spin supplementary conditions are constraints on spin degrees of freedom in classical relativity which restricts physical degrees of freedom to rotations. It is argued that the equivalent constraints in quantum field theory are the projection conditions on polarisation tensors, which remove timelike/longitudinal polarisations from the physical spectrum. The claim is supported by three examples of massive spinning particles coupled to electromagnetism: Dirac and Proca fields in quantum field theory, and $\mathcal{N} = 1$ worldline QFT for classical worldline theory. This suggests a resolution to the apparent discrepancy between effective field theory description of massive higher-spin fields~\cite{Bern:2020buy,Bern:2022kto} and post-Newtonian effective field theory of spinning classical particles~\cite{Levi:2015msa}, where the former admits more unfixed parameters compared to the latter; the additional parameters are fixed by projection conditions and therefore are not tunable parameters., Comment: version accepted to JHEP; title modified; footnote 1 on spin tensor definitions with boost-subtraction added; appendix D on classical EOM derivation from WQFT added; references added; 27 pages

The mass and spin of black holes (BHs) in binary systems may change due to the infall of gravitational-wave (GW) energy down the horizons. For spinning BHs, this effect enters at 2.5 post-Newtonian (PN) order relative to the leading-order energy flux at infinity. There is currently a discrepancy in the literature in the expressions of these horizon fluxes in the test-body limit at 4PN order (relative 1.5PN order). Here, we model the horizon absorption as tidal heating in an effective worldline theory of a spinning particle equipped with tidally-induced quadrupole and octupole moments. We match the tidal response to analytic solutions of the Teukolsky equation in a scattering scenario, and obtain general formulae for the evolution of mass and spin. We then specialize to the case of aligned-spin--quasi-circular binaries, obtaining the corresponding contributions to the GW phasing through 4PN order. Importantly, we find that the number of GW cycles due to horizon fluxes with masses observed by LIGO-Virgo-KAGRA detectors is about 2-3 orders of magnitude smaller than the other contributions to the phasing at the same PN order. Furthermore, in the test-body limit, we find full agreement with results obtained earlier from BH perturbation theory, with a small mass in an equatorial circular orbit treated as a source perturbing the Kerr metric. Thus, we weigh in on one side of the previous discrepancy., Comment: 29 Pages, 1 figure, 2 tables

We present the result of the quadratic-in-spin interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to NNNLO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. The gauge-invariant binding energy and the scattering angle, in special kinematic regimes and spin configurations, are explicitly derived. The results extend our earlier study on the spin-orbit interaction effects., Comment: 33 pages. arXiv admin note: text overlap with arXiv:2209.00611

We present the result of the spin-orbit interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to NNNLO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. We apply canonical transformations to eliminate the non-physical divergences and spurious logarithmic behaviours of the Hamiltonian, and use the latter to derive the gauge-invariant binding energy and the scattering angle, in special kinematic regimes., Comment: Generic Hamiltonian amended, satisfying Poincare Algebra, following arXiv:2208.14949 and arXiv:2210.17538. Ancillary files are revised

In certain scalar-field extensions to general relativity, scalar charges can develop on compact objects in an inspiraling binary -- an effect known as dynamical scalarization. This effect can be modeled using effective-field-theory methods applied to the binary within the post-Newtonian approximation. Past analytic investigations focused on the adiabatic (or quasi-stationary) case for quasi-circular orbits. In this work, we explore the full dynamical evolution around the phase transition to the scalarized regime. This allows for generic (eccentric) orbits and to quantify nonadiabatic (e.g., oscillatory) behavior during the phase transition. We also find that even in the circular-orbit case, the onset of scalarization can only be predicted reliably when taking the full dynamics into account, i.e., the adiabatic approximation is not appropriate. Our results pave the way for accurate post-Newtonian predictions for dynamical scalarization effects in gravitational waves from compact binaries., Comment: 15 pages, 11 figures. v2: matches published version

Upcoming observational runs of the LIGO-Virgo-KAGRA collaboration, and future gravitational-wave (GW) detectors on the ground and in space, require waveform models more accurate than currently available. High-precision waveform models can be developed by improving the analytical description of compact binary dynamics and completing it with numerical-relativity (NR) information. Here, we assess the accuracy of the recent results for the fourth post-Minkowskian (PM) conservative dynamics through comparisons with NR simulations for the circular-orbit binding energy and for the scattering angle. We obtain that the 4PM dynamics gives better agreement with NR than the 3PM dynamics, and that while the 4PM approximation gives comparable results to the third post-Newtonian (PN) approximation for bound orbits, it performs better for scattering encounters. Furthermore, we incorporate the 4PM results in effective-one-body (EOB) Hamiltonians, which improves the disagreement with NR over the 4PM-expanded Hamiltonian from $\sim 40\%$ to $\sim 10\%$, or $\sim 3\%$ depending on the EOB gauge, for an equal-mass binary, two GW cycles before merger. Finally, we derive a 4PN-EOB Hamiltonian for hyperbolic orbits, and compare its predictions for the scattering angle to NR, and to the scattering angle of a 4PN-EOB Hamiltonian computed for elliptic orbits., Comment: 21 pages, 9 figures, 1 ancillary file. v2: Matches published version. v3: correction in Appendix A

We perform tests of General Relativity (GR) with gravitational waves (GWs) from the inspiral stage of compact binaries using a theory-independent framework, which adds generic phase corrections to each multipole of a GR waveform model in frequency domain. This method has been demonstrated on LIGO-Virgo observations to provide stringent constraints on post-Newtonian predictions of the inspiral and to assess systematic biases that may arise in such parameterized tests. Here, we detail the anatomy of our framework for aligned-spin waveform models. We explore the effects of higher modes in the underlying signal on tests of GR through analyses of two unequal-mass, simulated binary signals similar to GW190412 and GW190814. We show that the inclusion of higher modes improves both the precision and the accuracy of the measurement of the deviation parameters. Our testing framework also allows us to vary the underlying baseline GR waveform model and the frequency at which the non-GR inspiral corrections are tapered off. We find that to optimize the GR test of high-mass binaries, comprehensive studies would need to be done to determine the best choice of the tapering frequency as a function of the binary's properties. We also carry out an analysis on the binary neutron-star event GW170817 to set bounds on the coupling constant $\alpha_0$ of Jordan-Fierz-Brans-Dicke gravity. We take two plausible approaches; in the first \emph{theory-agnostic} approach we find a bound $\alpha_0 \lesssim 2\times 10^{-1}$ from measuring the dipole-radiation for different neutron-star equations of state, while in the second \emph{theory-specific} approach we obtain $\alpha_0 \lesssim 4\times 10^{-1}$, both at $68\%$ credible level. These differences arise mainly due to different statistical hypotheses used for the analysis., Comment: 24 pages, 13 figures

As recent work continues to demonstrate, the study of relativistic scattering processes leads to valuable insights and computational tools applicable to the relativistic bound-orbit two-body problem. This is particularly relevant in the post-Minkowskian approach to the gravitational two-body problem, where the field has only recently reached a full description of certain physical observables for scattering orbits, including radiative effects, at the third post-Minkowskian (3PM) order. As an historically instructive simpler example, we consider here the analogous problem in electromagnetism in flat spacetime. We compute for the first time the changes in linear momentum of each particle and the total radiated linear momentum, in the relativistic classical scattering of two point-charges, at sixth order in the charges (analogous to 3PM order in gravity). We accomplish this here via direct iteration of the classical equations of motion, while making comparisons where possible to results from quantum scattering amplitudes, with the aim of contributing to the elucidation of conceptual issues and scalability on both sides. We also discuss further extensions to radiative quantities of recently established relations which analytically continue certain observables from the scattering regime to the regime of bound orbits, applicable for both the electromagnetic and gravitational cases., Comment: 25 pages

Picture yourself in the wave zone of a gravitational scattering event of two massive, spinning compact bodies (black holes, neutron stars or stars). We show that this system of genuine astrophysical interest enjoys a hidden $\mathcal{N}=2$ supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary $D$ spacetime dimensions. Using the ${\mathcal N}=2$ supersymmetric worldline action, augmented by finite-size corrections for the non-Kerr black hole case, we build a quadratic-in-spin extension to the worldline quantum field theory (WQFT) formalism introduced in our previous work, and calculate the two bodies' deflection and spin kick to sub-leading order in the post-Minkowskian expansion in Newton's constant $G$. For spins aligned to the normal vector of the scattering plane we also obtain the scattering angle. All $D$-dimensional observables are derived from an eikonal phase given as the free energy of the WQFT, that is invariant under the $\mathcal{N}=2$ supersymmetry transformations., Comment: 41 pages including references

With an increasing number of expected gravitational-wave detections of binary neutron star mergers, it is essential that gravitational-wave models employed for the analysis of observational data are able to describe generic compact binary systems. This includes systems in which the individual neutron stars are millisecond pulsars for which spin effects become essential. In this work, we perform numerical-relativity simulations of binary neutron stars with aligned and anti-aligned spins within a range of dimensionless spins of $\chi \sim [-0.28,0.58]$. The simulations are performed with multiple resolutions, show a clear convergence order and, consequently, can be used to test existing waveform approximants. We find that for very high spins gravitational-wave models that have been employed for the interpretation of GW170817 and GW190425 are not capable of describing our numerical-relativity dataset. We verify through a full parameter estimation study in which clear biases in the estimate of the tidal deformability and effective spin are present. We hope that in preparation of the next gravitational-wave observing run of the Advanced LIGO and Advanced Virgo detectors our new set of numerical-relativity data can be used to support future developments of new gravitational-wave models., Comment: 13 pages, 8 figures

The tidal response of a compact object is a key gravitational-wave observable encoding information about its interior. This link is subtle due to the nonlinearities of general relativity. We show that considering a scattering process bypasses challenges with potential ambiguities, as the tidal response is determined by the asymptotic in- and outgoing waves at null infinity. As an application of the general method, we analyze scalar waves scattering off a nonspinning black hole and demonstrate that the low-frequency expansion of the tidal response reproduces known results for the Love number and absorption. In addition, we discuss the definition of the response based on gauge-invariant observables obtained from an effective action description, and clarify the role of analytic continuation for robustly (i) extracting the response and the physical information it contains, and (ii) distinguishing high-order post-Newtonian corrections from finite-size effects in a binary system. Our work is important for interpreting upcoming gravitational-wave data for subatomic physics of ultradense matter in neutron stars, probing black holes and gravity, and looking for beyond-standard-model fields., Comment: v5, corrected typos, 29 pages, 2 figures

The recently established formalism of a worldline quantum field theory, which describes the classical scattering of massive bodies in Einstein gravity, is generalized up to quadratic order in spin -- for a pair of Kerr black holes revealing a hidden ${\mathcal N}=2$ supersymmetry. The far-field time-domain waveform of the gravitational waves produced in such a spinning encounter is computed at leading order in the post-Minkowskian (weak field, but generic velocity) expansion, and exhibits this supersymmetry. From the waveform we extract the leading-order total radiated angular momentum in a generic reference frame, and the total radiated energy in the center-of-mass frame to leading order in a low-velocity approximation., Comment: 7 pages + references, 2 figures

While most binary inspirals are expected to have circularized before they enter the LIGO/Virgo frequency band, a small fraction of those binaries could have non-negligible orbital eccentricity depending on their formation channel. Hence, it is important to accurately model eccentricity effects in waveform models used to detect those binaries, infer their properties, and shed light on their astrophysical environment. We develop a multipolar effective-one-body (EOB) eccentric waveform model for compact binaries whose components have spins aligned or anti-aligned with the orbital angular momentum. The waveform model contains eccentricity effects in the radiation-reaction force and gravitational modes through second post-Newtonian (PN) order, including tail effects, and spin-orbit and spin-spin couplings. We recast the PN-expanded, eccentric radiation-reaction force and modes in factorized form so that the newly derived terms can be directly included in the state-of-the-art, quasi-circular--orbit EOB model currently used in LIGO/Virgo analyses (i.e., the SEOBNRv4HM model)., Comment: 27 pages. v2: fixed typos, matches published version

Gravitational waves from neutron star binary inspirals contain information on strongly-interacting matter in unexplored, extreme regimes. Extracting this requires robust theoretical models of the signatures of matter in the gravitational-wave signals due to spin and tidal effects. In fact, spins can have a significant impact on the tidal excitation of the quasi-normal modes of a neutron star, which is not included in current state-of-the-art waveform models. We develop a simple approximate description that accounts for the Coriolis effect of spin on the tidal excitation of the neutron star's quadrupolar and octupolar fundamental quasi-normal modes and incorporate it in the SEOBNRv4T waveform model. We show that the Coriolis effect introduces only one new interaction term in an effective action in the co-rotating frame of the star, and fix the coefficient by considering the spin-induced shift in the resonance frequencies that has been computed numerically for the mode frequencies of rotating neutron stars in the literature. We investigate the impact of relativistic corrections due to the gravitational redshift and frame-dragging effects, and identify important directions where more detailed theoretical developments are needed in the future. Comparisons of our new model to numerical relativity simulations of double neutron star and neutron star-black hole binaries show improved consistency in the agreement compared to current models used in data analysis, Comment: 24 pages. v2: updated references and git link

Using the recently established formalism of a worldline quantum field theory (WQFT) description of the classical scattering of two spinless black holes, we compute the far-field time-domain waveform of the gravitational waves produced in the encounter at leading order in the post-Minkowskian (weak field, but generic velocity) expansion. We reproduce previous results of Kovacs and Thorne in a highly economic way. Then using the waveform we extract the leading-order total radiated angular momentum and energy (including differential results). Our work may enable crucial improvements of gravitational-wave predictions in the regime of large relative velocities., Comment: v3: additional supplementary material; accepted for publication in PRL

Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by tidal effects during a binary inspiral, leading to a potentially measurable effect in the gravitational-wave signal. We take an important step towards incorporating these effects in waveform models by developing a relativistic effective action for the gravitomagnetic dynamics that clarifies a number of subtleties. Working in the slow-rotation limit, we first consider the post-Newtonian approximation and explicitly derive the effective action from the equations of motion. We demonstrate that this formulation opens a way to compute mode frequencies, yields insights into the relevant matter variables, and elucidates the role of a shift symmetry of the fluid properties under a displacement of the gravitomagnetic mode amplitudes. We then construct a fully relativistic action based on the symmetries and a power counting scheme. This action involves four coupling coefficients that depend on the internal structure of the neutron star and characterize the key matter parameters imprinted in the gravitational waves. We show that, after fixing one of the coefficients by normalization, the other three directly involve the two kinds of gravitomagnetic Love numbers (static and irrotational), and the mode frequencies. We discuss several interesting features and dynamical consequences of this action, and analyze the frequency-domain response function (the frequency-dependent ratio between the induced flux quadrupole and the external gravitomagnetic field), and a corresponding Love operator representing the time-domain response. Our results provide the foundation for deriving precision predictions of gravitomagnetic effects, and the nuclear physics they encode, for gravitational-wave astronomy., Comment: 20 pages; v2: added time domain response/Love operator and discussion of electric driving, minor typos corrected, submitted to journal; v3: extended discussion; v4: published

A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of a pair of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field $h_{\mu\nu}(x)$ and position $x_i^\mu(\tau_i)$ of each black hole on equal footing. Using these both the next-order classical gravitational radiation $\langle h^{\mu\nu}(k)\rangle$ (previously unknown) and deflection $\Delta p_i^\mu$ from a binary black hole scattering event are obtained. The latter can also be obtained from the eikonal phase of a $2\to2$ scalar S-matrix, which we show to correspond to the free energy of the WQFT., Comment: v3: published version

The study of scattering encounters continues to provide new insights into the general relativistic two-body problem. The local-in-time conservative dynamics of an aligned-spin binary, for both unbound and bound orbits, is fully encoded in the gauge-invariant scattering-angle function, which is most naturally expressed in a post-Minkowskian (PM) expansion, and which exhibits a remarkably simple dependence on the masses of the two bodies (in terms of appropriate geometric variables). This dependence links the PM and small-mass-ratio approximations, allowing gravitational self-force results to determine new post-Newtonian (PN) information to all orders in the mass ratio. In this paper, we exploit this interplay between relativistic scattering and self-force theory to obtain the third-subleading (4.5PN) spin-orbit dynamics for generic spins, and the third-subleading (5PN) spin$_1$-spin$_2$ dynamics for aligned spins. We further implement these novel PN results in an effective-one-body framework, and demonstrate the improvement in accuracy by comparing against numerical-relativity simulations., Comment: 29 pages, 2 figures, supplemental material; v2: added references

We compute the first-order self-force contribution to Detweiler's redshift invariant for extended bodies endowed with both dipolar and quadrupolar structure (with spin-induced quadrupole moment) moving along circular orbits on a Schwarzschild background. Our analysis includes effects which are second order in spin, generalizing previous results for purely spinning particles. The perturbing body is assumed to move on the equatorial plane, the associated spin vector being orthogonal to it. The metric perturbations are obtained by using a standard gravitational self-force approach in a radiation gauge. Our results are accurate through the 6.5 post-Newtonian order, and are shown to reproduce the corresponding post-Newtonian expression for the same quantity computed by using the available Hamiltonian from an effective field theory approach for the dynamics of spinning binaries., Comment: 18 pages, revtex macros

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes., Comment: 8 pages, 2 figures. v2: matches version accepted in PRL

In a compact binary coalescence, the spins of the compact objects can have a significant effect on the orbital motion and gravitational-wave (GW) emission. For generic spin orientations, the orbital plane precesses, leading to characteristic modulations of the GW signal. The observation of precession effects is crucial to discriminate among different binary formation scenarios, and to carry out precise tests of General Relativity. Here, we work toward an improved description of spin effects in binary inspirals, within the effective-one-body (EOB) formalism, which is commonly used to build waveform models for LIGO and Virgo data analysis. We derive EOB Hamiltonians including the complete fourth post-Newtonian (4PN) conservative dynamics, which is the current state of the art. We place no restrictions on the spin orientations or magnitudes, or on the type of compact object (e.g., black hole or neutron star), and we produce the first generic-spin EOB Hamiltonians complete at 4PN order. We consider multiple spinning EOB Hamiltonians, which are more or less direct extensions of the varieties found in previous literature, and we suggest another simplified variant. Finally, we compare the circular-orbit, aligned-spin binding-energy functions derived from the EOB Hamiltonians to numerical-relativity simulations of the late inspiral. While finding that all proposed Hamiltonians perform reasonably well, we point out some interesting differences, which could guide the selection of a simpler, and thus faster-to-evolve EOB Hamiltonian to be used in future LIGO and Virgo inference studies., Comment: 26 pages, 6 figures, supplementary material. v2: fixed typos

The self-force program aims at accurately modeling relativistic two-body systems with a small mass ratio (SMR). In the context of the effective-one-body (EOB) framework, current results from this program can be used to determine the effective metric components at linear order in the mass ratio, resumming post-Newtonian (PN) dynamics around the test-particle limit in the process. It was shown in [Akcay et al., Phys. Rev. D 86 (2012)] that, in the original (standard) EOB gauge, the SMR contribution to the metric component $g^\text{eff}_{tt}$ exhibits a coordinate singularity at the light-ring (LR) radius. In this paper, we adopt a different gauge for the EOB dynamics and obtain a Hamiltonian that is free of poles at the LR, with complete circular-orbit information at linear order in the mass ratio and non-circular-orbit and higher-order-in-mass-ratio terms up to 3PN order. We confirm the absence of the LR-divergence in such an EOB Hamiltonian via plunging trajectories through the LR radius. Moreover, we compare the binding energies and inspiral waveforms of EOB models with SMR, PN and mixed SMR-3PN information on a quasi-circular inspiral against numerical-relativity predictions. We find good agreement between NR simulations and EOB models with SMR-3PN information for both equal and unequal mass ratios. In particular, when compared to EOB inspiral waveforms with only 3PN information, EOB Hamiltonians with SMR-3PN information improves the modeling of binary systems with small mass ratios $q \lesssim 1/3$, with a dephasing accumulated in $\sim$30 gravitational-wave (GW) cycles being of the order of few hundredths of a radian up to 4 GW cycles before merger., Comment: 16 pages, 5 figures

Gravitational wave observations can provide unprecedented insight into the fundamental nature of gravity and allow for novel tests of modifications to General Relativity. One proposed modification suggests that gravity may undergo a phase transition in the strong-field regime; the detection of such a new phase would constitute a smoking-gun for corrections to General Relativity at the classical level. Several classes of modified gravity predict the existence of such a transition - known as spontaneous scalarization - associated with the spontaneous symmetry breaking of a scalar field near a compact object. Using a strong-field-agnostic effective-field-theory approach, we show that all theories that exhibit spontaneous scalarization can also manifest dynamical scalarization, a phase transition associated with symmetry breaking in a binary system. We derive an effective point-particle action that provides a simple parametrization describing both phenomena, which establishes a foundation for theory-agnostic searches for scalarization in gravitational-wave observations. This parametrization can be mapped onto any theory in which scalarization occurs; we demonstrate this point explicitly for binary black holes with a toy model of modified electrodynamics., Comment: 15 pages, 5 figures. v3: added a figure, supplementary material, clarifications, and fixed typos. published

We demonstrate that a recently proposed classical double copy procedure to construct the effective action of two massive particles in dilaton-gravity from the analogous problem of two color charged particles in Yang-Mills gauge theory fails at next-to-next-to-leading orders in the post-Minkowskian (3PM) or post-Newtonian (2PN) expansions., Comment: v3: typos fixed, version published in PRD

Advanced methods for computing perturbative, quantum-gravitational scattering amplitudes show great promise for improving our knowledge of classical gravitational dynamics. This is especially true in the weak-field and arbitrary-speed (post-Minkowskian, PM) regime, where the conservative dynamics at 3PM order has been recently determined for the first time, via an amplitude calculation. Such PM results are most relevantly applicable to relativistic scattering (unbound orbits), while bound/inspiraling binary systems, the most frequent sources of gravitational waves for the LIGO and Virgo detectors, are most suitably modeled by the weak-field and slow-motion (post-Newtonian, PN) approximation. Nonetheless, it has been suggested that PM results can independently lead to improved modeling of bound binary dynamics, especially when taken as inputs for effective-one-body (EOB) models of inspiraling binaries. Here, we initiate a quantitative study of this possibility, by comparing PM, EOB and PN predictions for the binding energy of a two-body system on a quasi-circular inspiraling orbit against results of numerical relativity (NR) simulations. The binding energy is one of the two central ingredients (the other being the gravitational-wave energy flux) that enters the computation of gravitational waveforms employed by LIGO and Virgo detectors, and for (quasi-)circular orbits it provides an accurate diagnostic of the conservative sector of a model. We find that, whereas 3PM results do improve the agreement with NR with respect to 2PM (especially when used in the EOB framework), it is crucial to push PM calculations at higher orders if one wants to achieve better performances than current waveform models used for LIGO/Virgo data analysis., Comment: 13 pages, 7 figures. v2: published

Recently, the gravitational scattering of two black holes (BHs) treated at the leading order in the weak-field, or post-Minkowskian (PM), approximation to General Relativity has been shown to map bijectively onto a simpler effectively one-body process: the scattering of a test BH in a stationary BH spacetime. Here, for BH spins aligned with the orbital angular momentum, we propose a simple extension of that mapping to 2PM order. We provide evidence for the validity and utility of this 2PM mapping by demonstrating its compatibility with all known analytical results for the conservative local-in-time dynamics of binary BHs in the post-Newtonian (weak-field and slow-motion) approximation and, separately, in the test-BH limit. Our result could be employed in the construction of improved effective-one-body models for the conservative dynamics of inspiraling spinning binary BHs., Comment: v2: corrected misstatements in Sec. IV.C regarding the amount of residual gauge freedom within quasi-isotropic gauges for aligned-spin canonical Hamiltonians; no changes in any results or conclusions; improved discussion in Sections III-VI

In General Relativity and many modified theories of gravity, isolated black holes (BHs) cannot source massless scalar fields. Einstein-Maxwell-dilaton (EMd) theory is an exception: through couplings both to electromagnetism and (non-minimally) to gravity, a massless scalar field can be generated by an electrically charged BH. In this work, we analytically model the dynamics of binaries comprised of such scalar-charged ("hairy") BHs. While BHs are not expected to have substantial electric charge within the Standard Model of particle physics, nearly-extremally charged BHs could occur in models of minicharged dark matter and dark photons. We begin by studying the test-body limit for a binary BH in EMd theory, and we argue that only very compact binaries of nearly-extremally charged BHs can manifest non-perturbative phenomena similar to those found in certain scalar-tensor theories. Then, we use the post-Newtonian approximation to study the dynamics of binary BHs with arbitrary mass ratios. We derive the equations governing the conservative and dissipative sectors of the dynamics at next-to-leading order, use our results to compute the Fourier-domain gravitational waveform in the stationary-phase approximation, and compute the number of useful cycles measurable by the Advanced LIGO detector. Finally, we construct two effective-one-body (EOB) Hamiltonians for binary BHs in EMd theory: one that reproduces the exact test-body limit and another whose construction more closely resembles similar models in General Relativity, and thus could be more easily integrated into existing EOB waveform models used in the data analysis of gravitational-wave events by the LIGO and Virgo collaborations., Comment: 36 pages, 12 figures, updated to match published version

The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading order effect in the phase of gravitational waves emitted by extreme-mass-ratio inspirals (EMRIs), which are expected to become observable by the LISA space mission. Additionally, exploring the Hamiltonian formalism for spinning bodies is important for the construction of the so-called Effective-One-Body waveform models that should eventually cover all mass ratios. The MPD equations require supplementary conditions determining the frame in which the moments of the body are computed. We review various choices of these supplementary spin conditions and their properties. Then, we give Hamiltonians either in proper-time or coordinate-time parametrization for the Tulczyjew-Dixon, Mathisson-Pirani, and Kyrian-Semer\'ak conditions. Finally, we also give canonical phase-space coordinates parametrizing the spin tensor. We demonstrate the usefulness of the canonical coordinates for symplectic integration by constructing Poincar\'e surfaces of section for spinning bodies moving in the equatorial plane in Schwarzschild space-time. We observe the motion to be essentially regular for EMRI-ranges of the spin, but for larger values the Poincar\'e surfaces of section exhibit the typical structure of a weakly chaotic system. A possible future application of the numerical integration method is the inclusion of spin effects in EMRIs at the precision requirements of LISA., Comment: 37 pages, 2 figures. Accepted at CQG

We compute the classical effective action of color charges moving along worldlines by integrating out the Yang-Mills gauge field to next-to-leading order in the coupling. An adapted version of the Bern-Carrasco-Johansson (BCJ) double-copy construction known from quantum scattering amplitudes is then applied to the Feynman integrands, yielding the prediction for the classical effective action of point masses in dilaton gravity. We check the validity of the result by independently constructing the effective action in dilaton gravity employing field redefinitions and gauge choices that greatly simplify the perturbative construction. Complete agreement is found at next-to-leading order. Finally, upon performing the post-Newtonian expansion of our result, we find agreement with the corresponding action of scalar-tensor theories known from the literature. Our results represent a proof of concept for the classical double-copy construction of the gravitational effective action and provides another application of a BCJ-like double copy beyond scattering amplitudes., Comment: 23 pages. v2: some typos fixed. v3: published version

We determine the binding energy, the total gravitational wave energy flux, and the gravitational wave modes for a binary of rapidly spinning black holes, working in linearized gravity and at leading orders in the orbital velocity, but to all orders in the black holes' spins. Though the spins are treated nonperturbatively, surprisingly, the binding energy and the flux are given by simple analytical expressions which are finite (respectively third- and fifth-order) polynomials in the spins. Our final results are restricted to the important case of quasi-circular orbits with the black holes' spins aligned with the orbital angular momentum., Comment: 16 pages, 1 figure; updated to match published version

Gravitational waves can be used to test general relativity (GR) in the highly dynamical strong-field regime. Scalar-tensor theories of gravity are natural alternatives to GR that can manifest nonperturbative phenomena in neutron stars (NSs). One such phenomenon, known as dynamical scalarization, occurs in coalescing binary NS systems. Ground-based gravitational-wave detectors may be sensitive to this effect, and thus could potentially further constrain scalar-tensor theories. This type of analysis requires waveform models of dynamically scalarizing systems; in this work we devise an analytic model of dynamical scalarization using an effective action approach. For the first time, we compute the Newtonian-order Hamiltonian describing the dynamics of a dynamically scalarizing binary in a self-consistent manner. Despite only working to leading order, the model accurately predicts the frequency at which dynamical scalarization occurs. In conjunction with Landau theory, our model allows one to definitively establish dynamical scalarization as a second-order phase transition. We also connect dynamical scalarization to the related phenomena of spontaneous scalarization and induced scalarization; these phenomena are naturally encompassed into our effective action approach., Comment: Updated to match published version

We present a new public package "EFTofPNG" for high precision computation in the effective field theory of post-Newtonian (PN) Gravity, including spins. We created this package in view of the timely need to publicly share automated computation tools, which integrate the various types of physics manifested in the expected increasing influx of gravitational wave (GW) data. Hence, we created a free and open source package, which is self-contained, modular, all-inclusive, and accessible to the classical Gravity community. The "EFTofPNG" Mathematica package also uses the power of the "xTensor" package, suited for complicate tensor computation, where our coding also strategically approaches the generic generation of Feynman contractions, which is universal to all perturbation theories in physics, by efficiently treating n-point functions as tensors of rank n. The package currently contains four independent units, which serve as subsidiaries to the main one. Its final unit serves as a pipeline chain for the obtainment of the final GW templates, and provides the full computation of all derivatives and gauge invariant physical observables of interest. The upcoming "EFTofPNG" package version 1.0 should cover the point mass sector, and all the spin sectors, up to the fourth PN order, and the two-loop level. We expect and strongly encourage public development of the package to improve its efficiency, and to extend it to further PN sectors, and observables useful for the waveform modeling., Comment: Invited article to special issue on "Approaches to the two-body problem". 15 pages, 1 figure. published code available as a public repository through GitHub: https://github.com/miche-levi/pncbc-eftofpng

Binary systems containing boson stars---self-gravitating configurations of a complex scalar field--- can potentially mimic black holes or neutron stars as gravitational-wave sources. We investigate the extent to which tidal effects in the gravitational-wave signal can be used to discriminate between these standard sources and boson stars. We consider spherically symmetric boson stars within two classes of scalar self-interactions: an effective-field-theoretically motivated quartic potential and a solitonic potential constructed to produce very compact stars. We compute the tidal deformability parameter characterizing the dominant tidal imprint in the gravitational-wave signals for a large span of the parameter space of each boson star model. We find that the tidal deformability for boson stars with a quartic self-interaction is bounded below by $\Lambda_{\rm min}\approx 280$ and for those with a solitonic interaction by $\Lambda_{\rm min}\approx 1.3$. Employing a Fisher matrix analysis, we estimate the precision with which Advanced LIGO and third-generation detectors can measure these tidal parameters using the inspiral portion of the signal. We discuss a new strategy to improve the distinguishability between black holes/neutrons stars and boson stars by combining deformability measurements of each compact object in a binary system, thereby eliminating the scaling ambiguities in each boson star model. Our analysis shows that current-generation detectors can potentially distinguish boson stars with quartic potentials from black holes, as well as from neutron-star binaries if they have either a large total mass or a large mass ratio. Discriminating solitonic boson stars from black holes using only tidal effects during the inspiral will be difficult with Advanced LIGO, but third-generation detectors should be able to distinguish between binary black holes and these binary boson stars., Comment: 18 pages, 8 figures. Submitted to Physical Review D

Tidal effects have an important impact on the late inspiral of compact binary systems containing neutron stars. Most current models of tidal deformations of neutron stars assume that the tidal bulge is directly related to the tidal field generated by the companion, with a constant response coefficient. However, if the orbital motion approaches a resonance with one of the internal modes of the neutron star, this adiabatic description of tidal effects starts to break down, and the tides become dynamical. In this paper, we consider dynamical tides in general relativity due to the quadrupolar fundamental oscillation mode of a neutron star. We devise a description of the effects of the neutron star's finite size on the orbital dynamics based on an effective point-particle action augmented by dynamical quadrupolar degrees of freedom. We analyze the post-Newtonian and test-particle approximations of this model and incorporate the results into an effective-one-body Hamiltonian. This enables us to extend the description of dynamical tides over the entire inspiral. We demonstrate that dynamical tides give a significant enhancement of matter effects compared to adiabatic tides, at least for neutron stars with large radii and for low mass-ratio systems, and should therefore be included in accurate models for gravitational-wave data analysis., Comment: 29 pages, 5 figures. v2: published

In this work we complete the spin-dependent conservative dynamics of inspiralling compact binaries at the fourth post-Newtonian order, and in particular the derivation of the next-to-next-to-leading order spin-squared interaction potential. We derive the physical equations of motion of the position and the spin from a direct variation of the action. Further, we derive the quadratic-in-spin Hamiltonians, as well as their expressions in the center-of-mass frame. We construct the conserved integrals of motion, which form the Poincar\'e algebra. This construction provided a consistency check for the validity of our result, which is crucial in particular in the current absence of another independent derivation of the next-to-next-to-leading order spin-squared interaction. Finally, we provide here the complete gauge-invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to the fourth post-Newtonian order. These high post-Newtonian orders, in particular taking into account the spins of the binary constituents, will enable to gain more accurate information on the constituents from even more sensitive gravitational-wave detections to come., Comment: 23 pages, published

We discuss the effects of the black holes' spin-multipole structure in the orbital dynamics of binary black holes according to general relativity, focusing on the leading-post-Newtonian-order couplings at each order in an expansion in the black holes' spins. We first review previous widely confirmed results up through fourth order in spin, observe suggestive patterns therein, and discuss how the results can be extrapolated to all orders in spin with minimal information from the test-body limit. We then justify this extrapolation by providing a complete derivation within the post-Newtonian framework of a canonical Hamiltonian for a binary black hole, for generic orbits and spin orientations, which encompasses the leading post-Newtonian orders at all orders in spin. At the considered orders, the results reveal a precise equivalence between arbitrary-mass-ratio two-spinning-black-hole dynamics and the motion of a test black hole in a Kerr spacetime, as well as an intriguing relationship to geodesic motion in a Kerr spacetime., Comment: 12 pages, 3 figures; minor typos corrected; reflects changes in published version

Extracting the unique information on ultradense nuclear matter from the gravitational waves emitted by merging, neutron-star binaries requires robust theoretical models of the signal. We develop a novel effective-one-body waveform model that includes, for the first time, dynamic (instead of only adiabatic) tides of the neutron star, as well as the merger signal for neutron-star--black-hole binaries. We demonstrate the importance of the dynamic tides by comparing our model against new numerical-relativity simulations of nonspinning neutron-star--black-hole binaries spanning more than 24 gravitational-wave cycles, and to other existing numerical simulations for double neutron-star systems. Furthermore, we derive an effective description that makes explicit the dependence of matter effects on two key parameters: tidal deformability and fundamental oscillation frequency.

We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This requires a careful analysis of how changes of the spin supplementary condition are related to shifts of the body's representative worldline and transformations of the body's multipole moments, and we employ bitensor calculus for a precise framing of this analysis. We apply the result to the case of the Kerr spacetime and thereby compute an explicit canonical Hamiltonian for the test-body limit of the spinning two-body problem in general relativity, valid for generic orbits and spin orientations, to quadratic order in the test spin. This fully relativistic Hamiltonian is then expanded in post-Newtonian orders and in powers of the Kerr spin parameter, allowing comparisons with the test-mass limits of available post-Newtonian results. Both the fully relativistic Hamiltonian and the results of its expansion can inform the construction of waveform models, especially effective-one-body models, for the analysis of gravitational waves from compact binaries., Comment: v3: corrected errors in Eq. (D8); see Note Added on page 19