Search

In this paper we derive for the first time the complete gravitational quartic-in-spin interaction of generic compact binaries at the next-to-leading order in the post-Newtonian (PN) expansion. The derivation builds on the effective field theory for gravitating spinning objects, and its recent extensions, in which new type of worldline couplings should be considered, as well as on the extension of the effective action of a spinning particle to quadratic order in the curvature. The latter extension entails a new Wilson coefficient that appears in this sector. This work pushes the precision frontier with spins at the fifth PN (5PN) order for maximally-spinning compact objects, and at the same time informs us of the gravitational Compton scattering with higher spins. [ABSTRACT FROM AUTHOR]

It was recently shown that (near-)extremal Kerr black holes are sensitive probes of small higher-derivative corrections to general relativity. In particular, these corrections produce diverging tidal forces on the horizon in the extremal limit. We show that adding a black hole charge makes this effect qualitatively stronger. Higher-derivative corrections to the Kerr-Newman solution produce tidal forces that scale inversely in the black hole temperature. We find that, unlike the Kerr case, for realistic values of the black hole charge large tidal forces can arise before quantum corrections due to the Schwarzian mode become important, so that the near-horizon behavior of the black hole is dictated by higher-derivative terms in the effective theory. [ABSTRACT FROM AUTHOR]

The static Love numbers of four-dimensional asymptotically flat, isolated, general-relativistic black holes are known to be identically vanishing. The Love symmetry proposal suggests that such vanishings are addressed by selection rules following from the emergence of an enhanced ("Love") symmetry in the near-zone region; more specifically, it is the fact that the black hole perturbations belong to a highest-weight representation of this near-zone symmetry, rather than the existence of the Love symmetry itself, that outputs the vanishings of the corresponding Love numbers. In higher spacetime dimensions, some towers of magic zeroes with regards to the black hole response problem have also been reported for scalar, electromagnetic and gravitational perturbations of the Schwarzschild-Tangherlini black hole. Here, we extend these results by supplementing with p-form perturbations of the Schwarzschild-Tangherlini black hole. We furthermore analytically extract the static Love numbers and the leading order dissipation numbers associated with spin-0 scalar and spin-2 tensor-type tidal perturbations of the higher-dimensional Reissner-Nordström black hole. We find that Love symmetries exist and that the vanishings of the static Love numbers are captured by representation theory arguments even for these higher spin perturbations of the higher-dimensional spherically symmetric black holes of General Relativity. Interestingly, these near-zone structures acquire extensions to Witt algebras. Our setup allows to also study the p-form response problem of a static spherically symmetric black hole in a generic theory of gravity. We perform explicit computations for some black holes in the presence of string-theoretic corrections and investigate under what geometric conditions Love symmetries emerge in the near-zone. [ABSTRACT FROM AUTHOR]

We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects. The construction relies on the introduction of a new covariant derivative, which we name "classical spin covariant derivative", that is compatible with the three-point interaction of the Kerr solution with the gauge field. The resulting Lagrangian, besides the correct three-point coupling, predicts a unique choice for contact terms and therefore it can be used to compute higher-point amplitudes such as the Compton, unaffected by spurious poles. Using double copy techniques we use this theory to extract gravity amplitudes and observables that are relevant to describe Kerr binary dynamics to all orders in the spin. In particular, we compute the 2PM (O ( G N 2 )) 2 → 2 elastic scattering amplitude between two classically spinning objects to all orders in the spin and use it to extract the 2PM scattering angle. [ABSTRACT FROM AUTHOR]

We present the result of the quadratic-in-spin interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to N3LO 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. [ABSTRACT FROM AUTHOR]

Using a heavy-mass effective field theory (HEFT), we study gravitational-wave emission in the scattering of two spinless black holes or neutron stars of arbitrary masses at next-to-leading order in the Post-Minkowskian expansion. We compute the contributions to the one-loop scattering amplitude with four scalars and one graviton which are relevant to the calculation of the waveforms, also presenting expressions of classical tree-level amplitudes with four scalars and up to two radiated gravitons. The latter are obtained using a novel on-shell recursion relation for classical amplitudes with four scalars and an arbitrary number of gravitons. Our one-loop five-point amplitude is expressed in terms of a single family of master integrals with the principal value prescription for linearised massive propagators, which we evaluate using differential equations. In our HEFT approach, soft/heavy-mass expansions of complete integrands are avoided, and all hyper-classical iterations and quantum corrections are dropped at the diagrammatic level, thereby computing directly contributions to classical physics. Our result exhibits the expected factorisation of infrared divergences, the correct soft limits, and highly nontrivial cancellations of spurious poles. Finally, using our amplitude result we compute numerically the corresponding next-to-leading corrections to the spectral waveforms and the far-field time-domain waveforms using the Newman-Penrose scalar Ψ4. [ABSTRACT FROM AUTHOR]

We present the derivation of the third subleading order (N3LO) spin-orbit interaction at the state of the art of post-Newtonian (PN) gravity via the EFT of spinning objects. The present sector contains the largest and most elaborate collection of Feynman graphs ever tackled to date in sectors with spin, and in all PN sectors up to third subleading order. Our computations are carried out via advanced multi-loop methods. Their most demanding aspect is the imperative transition to a generic dimension across the whole derivation, due to the emergence of dimensional-regularization poles across all loop orders as of the N3LO sectors. At this high order of sectors with spin, it is also critical to extend the formal procedure for the reduction of higher-order time derivatives of spin variables beyond linear order for the first time. This gives rise to a new unique contribution at the present sector. The full interaction potential in Lagrangian form and the general Hamiltonian are provided here for the first time. The consequent gravitational-wave (GW) gauge-invariant observables are also derived, including relations among the binding energy, angular momentum, and emitted frequency. Complete agreement is found between our results, and the binding energy of GW sources, and also with the extrapolated scattering angle in the scattering problem, derived via traditional GR. In contrast with the latter derivation, our framework is free-standing and generic, and has provided theory and results, which have been critical to establish the state of the art, and to push the precision frontier for the measurement of GWs. [ABSTRACT FROM AUTHOR]

In recent work, Hollands, Kovács and Reall have built on previous work of Wall to provide a definition of dynamical black hole entropy for gravitational effective field theories (EFTs). This entropy satisfies a second law of black hole mechanics to quadratic order in perturbations around a stationary black hole. We determine the explicit form of this entropy for the EFT of 4d vacuum gravity including terms in the action with up to 6 derivatives. An open question concerns the gauge invariance of this definition of black hole entropy. We show that gauge invariance holds for the EFT of vacuum gravity with up to 6 derivatives but demonstrate that it can fail when 8 derivative terms are included. We determine an entropy for Einstein-Gauss-Bonnet theory by treating it as an EFT with vanishing 6 derivative terms. [ABSTRACT FROM AUTHOR]

We study the classical double copy of massive spinning objects in the worldline quantum field theories (WQFT) formalism. We couple the N = 1 supersymmetric model to a Yang-Mills background to describe the propagation of a spin-half particle interacting with gluons. At the classical level, this model captures physical effects up to linear order in spin. We propose a double copy relation to map the spin tensors to the gravitation side. Enforcing R-symmetry and supersymmetry (SUSY) on the double copy integrands, we find that the gravitational theory is the N = 2 particle coupled to dilaton-gravity (DG). We check the double copy prescription for the eikonal phase up to next-to-leading order and for radiation at leading order in coupling constants, finding that the Grassmann nature of the spin tensor in WQFT plays a crucial role in finding full agreement with direct calculation in the N = 2 model. We show how to deform the SUSY charges of the free theory to include DG. Since the constraints algebra is first class, the worldline model can be quantized, describing the propagation of a massive vector field coupled to DG, in agreement with the literature. In addition, we investigate the double copy without preserving SUSY and R-symmetry, finding that the B-field also couples to the worldline. [ABSTRACT FROM AUTHOR]

We present the result of the spin-orbit interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to N3LO 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. [ABSTRACT FROM AUTHOR]

We generalize the world line EFT formalism to account for parity violating finite size effects. Results are presented for potentials and radiating moments of a binary inspiral for the parity conserving sector, and agreement is found with, previous calculations. Furthermore, we generate new results in this sector, calculating the current quadrupole moment induced by finite size gravitomagnetic effects. We also present novel results for parity violating sources, which might be due to beyond standard model physics, and show that they generate GW signals with the unique signature that the current-moment appears at 0.5PN order earlier relative to the mass-moment in the PN expansion. Parity violation also induces a new type of potential, which is proportional to the S ∙ r. Finally, we present new results for the dissipative force for parity violating constituents, which leads to the curious signature of a force normal to the orbit. [ABSTRACT FROM AUTHOR]

We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for N non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for N > 2 are described including the subtraction of tree-like iteration contributions and the calculation of non-trivial many-body Fourier transform integrals needed to construct position space potentials. A new approach to calculating these integrals as an expansion in the hierarchical limit is described based on the method of regions. As an explicit example, we present the O (G2) 3-body momentum space potential in general relativity as well as for charged bodies in Einstein-Maxwell. The result is shown to be in perfect agreement with previous post-Newtonian calculations in general relativity up to O (G2v4). Furthermore, in appropriate limits the result is shown to agree perfectly with relativistic probe scattering in multi-center extremal black hole backgrounds and with the scattering of slowly-moving extremal black holes in the moduli space approximation. [ABSTRACT FROM AUTHOR]

We employ the “KMOC” formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop). We do this in electrodynamics and gravity. The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop. Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order. We carry out our computations both using a unitarity based framework and Feynman diagrammatic approach which relies on scattering amplitudes computed on fixed backgrounds. [ABSTRACT FROM AUTHOR]

Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2, ℝ) symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2, ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2, ℝ) representations. It is this highest weight properety that forces the static Love numbers to vanish. We find that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. This relation is simplest for extremal charged spherically symmetric (Reissner-Nordström) solutions, where the Love symmetry exactly reduces to the isometry of the near horizon AdS2 throat. For rotating (Kerr-Newman) black holes one is lead to consider an infinite-dimensional SL(2, ℝ) ⋉ U ̂ 1 V extension of the Love symmetry. It contains three physically distinct subalgebras: the Love algebra, the Starobinsky near zone algebra, and the near horizon algebra that becomes the Bardeen-Horowitz isometry in the extremal limit. We also discuss other aspects of the Love symmetry, such as the geometric meaning of its generators for spin weighted fields, connection to the no-hair theorems, non-renormalization of Love numbers, its relation to (non-extremal) Kerr/CFT correspondence and prospects of its existence in modified theories of gravity. [ABSTRACT FROM AUTHOR]

The classical scattering of spinning objects is well described by the spinor-helicity formalism for heavy particles. Using these variables, we derive spurious-pole-free, all-spin opposite-helicity Compton amplitudes (factorizing on physical poles to the minimal, all-spin three-point amplitudes) in the classical limit for QED, QCD, and gravity. The cured amplitudes are subject to deformations by contact terms, the vast majority of whose contributions we can fix by imposing a relation between spin structures — motivated by lower spin multipoles of black hole scattering — at the second post-Minkowskian (2PM) order. For QED and gravity, this leaves a modest number of unfixed coefficients parametrizing contact-term deformations, while the QCD amplitude is uniquely determined. Our gravitational Compton amplitude allows us to push the state-of-the-art of spinning-2PM scattering to any order in the spin vectors of both objects; we present results here and in the supplementary material file 2PMSpin8Aux.nb up to eighth order in the spin vectors. Interestingly, despite leftover coefficients in the Compton amplitude, imposing the aforementioned relation between spin structures uniquely fixes some higher-spin parts of the 2PM amplitude. [ABSTRACT FROM AUTHOR]

Abstract In this paper we derive for the first time the complete gravitational quartic-in-spin interaction of generic compact binaries at the next-to-leading order in the post-Newtonian (PN) expansion. The derivation builds on the effective field theory for gravitating spinning objects, and its recent extensions, in which new type of worldline couplings should be considered, as well as on the extension of the effective action of a spinning particle to quadratic order in the curvature. The latter extension entails a new Wilson coefficient that appears in this sector. This work pushes the precision frontier with spins at the fifth PN (5PN) order for maximally-spinning compact objects, and at the same time informs us of the gravitational Compton scattering with higher spins.

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 N = 2 supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary D spacetime dimensions. Using the 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 N = 2 supersymmetry transformations. [ABSTRACT FROM AUTHOR]

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton’s contant G and at all orders in the velocities, using the Effective Field Theory worldline approach. Following [1], we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in G, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes. [ABSTRACT FROM AUTHOR]

We generalize the worldline EFT formalism developed in [4–9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin. We present results for the rate of change of mass and angular momentum in a background field and find agreement with previous calculations obtained by different techniques. We also present new results for both the non-conservative equations of motion and power loss/gain for a binary inspiral, which start at 5PN and 2.5PN order respectively and manifest the Penrose process. [ABSTRACT FROM AUTHOR]

It was shown recently that the static tidal response coefficients, called Love numbers, vanish identically for Kerr black holes in four dimensions. In this work, we confirm this result and extend it to the case of spin-0 and spin-1 perturbations. We compute the static response of Kerr black holes to scalar, electromagnetic, and gravitational fields at all orders in black hole spin. We use the unambiguous and gauge-invariant definition of Love numbers and their spin-0 and spin-1 analogs as Wilson coefficients of the point particle effective field theory. This definition also allows one to clearly distinguish between conservative and dissipative response contributions. We demonstrate that the behavior of Kerr black hole responses to spin-0 and spin-1 fields is very similar to that of the spin-2 perturbations. In particular, static conservative responses vanish identically for spinning black holes. This implies that vanishing Love numbers are a generic property of black holes in four-dimensional general relativity. We also show that the dissipative part of the response does not vanish even for static perturbations due to frame-dragging. [ABSTRACT FROM AUTHOR]

A factorisation property of Feynman diagrams in the context the Effective Field Theory approach to the compact binary problem has been recently employed to efficiently determine the static sector of the potential at fifth post-Newtonian (5PN) order. We extend this procedure to the case of non-static diagrams and we use it to fix, by means of elementary algebraic manipulations, the value of more than one thousand diagrams at 5PN order, that is a substantial fraction of the diagrams needed to fully determine the dynamics at 5PN. This procedure addresses the redundancy problem that plagues the computation of the binding energy with respect to more “efficient” observables like the scattering angle, thus making the EFT approach in harmonic gauge at least as scalable as the others methods. [ABSTRACT FROM AUTHOR]

In this work we derive for the first time the complete gravitational cubic-in-spin effective action at the next-to-leading order in the post-Newtonian (PN) expansion for the interaction of generic compact binaries via the effective field theory for gravitating spinning objects, which we extend in this work. This sector, which enters at the fourth and a half PN (4.5PN) order for rapidly-rotating compact objects, completes finite-size effects up to this PN order, and is the first sector completed beyond the current state of the art for generic compact binary dynamics at the 4PN order. At this order in spins with gravitational nonlinearities we have to take into account additional terms, which arise from a new type of worldline couplings, due to the fact that at this order the Tulczyjew gauge for the rotational degrees of freedom, which involves the linear momentum, can no longer be approximated only in terms of the four-velocity. One of the main motivations for us to tackle this sector is also to see what happens when we go to a sector, which corresponds to the gravitational Compton scattering with quantum spins larger than one, and maybe possibly also get an insight on the inability to uniquely fix its amplitude from factorization when spins larger than two are involved. A general observation that we can clearly make already is that even-parity sectors in the order of the spin are easier to handle than odd ones. In the quantum context this corresponds to the greater ease of dealing with bosons compared to fermions. [ABSTRACT FROM AUTHOR]

We apply the classical double copy to the calculation of self-energy of composite systems with multipolar coupling to gravitational field, obtaining next-to-leading order results in the gravitational coupling GN by generalizing color to kinematics replacement rules known in literature. When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and then re-absorbed by the same source. These processes contribute to the conservative two-body dynamics and the present work represents a decisive step towards the systematic use of double copy within the multipolar post-Minkowskian expansion. [ABSTRACT FROM AUTHOR]

We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the test-particle limit in which the system is fully characterized by a particle propagating in a Schwarzschild spacetime. We assume a general choice of graviton field basis and gauge fixing that contains as a subset the well-known deDonder gauge and its various cousins. As a highly nontrivial consistency check, all gauge parameters evaporate from the final answer. Moreover, our result exactly matches that of Bern et al. [39], here verified up to sixth post-Newtonian order while also reproducing the same unique velocity resummation at third post-Minkowksian order. [ABSTRACT FROM AUTHOR]

In this work we propose to use leading singularities to obtain the classical pieces of amplitudes of two massive particles whose only interaction is gravitational. Leading singularities are generalizations of unitarity cuts. At one-loop we find that leading singularities obtained by multiple discontinuities in the t-channel contain all the classical information. As the main example, we show how to obtain a compact formula for the fully relativistic classical one-loop contribution to the scattering of two particles with different masses. The non-relativistic limit of the leading singularity agrees with known results in the post-Newtonian expansion. We also compute a variety of higher loop leading singularities including some all-loop families and study some of their properties. [ABSTRACT FROM AUTHOR]

The recent direct observation of gravitational waves (GW) from merging black holes opens up the possibility of exploring the theory of gravity in the strong regime at an unprecedented level. It is therefore interesting to explore which extensions to General Relativity (GR) could be detected. We construct an Effective Field Theory (EFT) satisfying the following requirements. It is testable with GW observations; it is consistent with other experiments, including short distance tests of GR; it agrees with widely accepted principles of physics, such as locality, causality and unitarity; and it does not involve new light degrees of freedom. The most general theory satisfying these requirements corresponds to adding to the GR Lagrangian operators constructed out of powers of the Riemann tensor, suppressed by a scale comparable to the curvature of the observed merging binaries. The presence of these operators modifies the gravitational potential between the compact objects, as well as their effective mass and current quadrupoles, ultimately correcting the waveform of the emitted GW. [ABSTRACT FROM AUTHOR]