arXiv subjects

Rafael A. Porto

Publications and source records attributed to Rafael A. Porto.

At least 19 recordsLinked to original sources

arXiv2026

Trails of clouds in binary black holes

Superradiant instabilities of rotating black holes can give rise to long-lived bosonic clouds, offering natural laboratories to probe ultralight particles across a wide range of parameter space. The presence of a companion can dramatically impact both the cloud's evolution and the binary's orbital dynamics, generating a trail of feedback effects that require detailed modelling. Using a worldline effective field theory approach, we develop a systematic framework for binaries on generic (eccentric and inclined) orbits, capturing both resonant and non-resonant transitions without relying solely on balance laws. We demonstrate the existence of ``co-rotating'' floating orbits that can deplete the cloud prior to entering the detector's band, triggering eccentricity growth towards a sequence of fixed points. Likewise, we show that ``counter-rotating'' orbits can also deplete the cloud, driving (unbounded) growth of eccentricity. Furthermore, we uncover novel features tied to orbital inclination. Depending on the mass ratio, equatorial orbits can become unstable, and fixed points may arise not only for aligned or anti-aligned configurations but, strikingly, also at intermediate inclinations. We derive flow equations governing spin-orbit misalignment and eccentricity and identify distinctive signatures that can reveal the presence of boson clouds in the binary's history, as well as key features of possible in-band transitions. These results refine and extend earlier work, yielding a more faithful description of the imprints of ultralight particles in gravitational-wave signals from binary black holes, signatures that are within reach of future detectors such as LISA, Cosmic Explorer, and the Einstein~Telescope.

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arXiv2026

Black Hole Dynamics at Fifth Post-Newtonian Order

Using the worldline action in [2409.05860], we derive the total even-in-velocity (relative) impulse, scattering angle, and time delay at fifth post-Newtonian (5PN) order, including radiation-reaction and hereditary contributions at ${\cal O}(G^5ν^2)$ and ${\cal O}(G^6ν^2)$. We introduce an isotropic-like description which, together with the associated losses of energy and angular momentum, fixes the evolution of the system from scattering data. This framework opens the door to an unambiguous characterization of the underlying two-body dynamics solely in terms of scattering observables. Following [2409.05860], we isolate a conservative component using Feynman's $i0^+$ prescription. This sector contains both "tail-like" and "memory-like" contributions, the latter being nonlocal in time and described by a double Principal-Value integral. Owing to the local-in-time character of the corresponding (in-in) action, we establish a systematic procedure that is consistent with Feynman's prescription while preserving the complete local dynamics. This provides a universal contribution to the conservative (isotropic) Hamiltonian at 5PN order and, as a byproduct, also fixes the value of the Effective One Body coefficients $\{{\bar d}_{5{\rm loc}}, a_{6{\rm loc}}\}$ consistently with the Tutti-Frutti framework. For completeness, we analyse the "$γ\text{-}3$" prescription introduced in recent post-Minkowskian computations. When implemented in our formalism, we find exact agreement over the overlapping regime of validity. In contrast, Feynman's prescription yields a (local) memory-like contribution with the opposite sign at ${\cal O}(G^5ν^2)$. We also find that an analogous $γ\text{-}3$ rerouting at ${\cal O}(G^6ν^2)$ would be incompatible with the conjecture that all $π^2$ terms arise solely from the potential region, while Feynman's formulation preserves this expectation.

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arXiv2026

Nonlocal-in-time tail effects in gravitational scattering to fifth Post-Minkowskian and tenth self-force orders

Using the worldline effective field theory formalism, we derive the nonlocal-in-time conservative contributions arising from tail effects in gravitational scattering to fifth Post-Minkowskian (5PM) and tenth self-force (10SF) orders. The result features multiple polylogarithms of up to weight three. This challenging computation relies on state-of-the-art integration techniques, including a novel integration-by-parts algorithm: the Sparse Integral Reducer (SpideR). We find perfect agreement in the overlap with all existing literature through sixth post-Newtonian order. The results presented here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at 5PM order.

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arXiv2025

Local-in-Time Conservative Binary Dynamics at Fifth Post-Minkowskian and First Self-Force Orders

We report the local-in-time conservative dynamics of nonspinning binary systems at fifth Post-Minkowskian (5PM) and first self-force (1SF) orders. This follows from an explicit calculation of the 5PM/1SF nonlocal-in-time tail-type contribution to the deflection angle via worldline effective field theory techniques. Proceeding as in [2403.04853], we subtract the nonlocal tail terms from the result in [2403.07781] and reconstruct a local-in-time Hamiltonian in isotropic gauge -- valid for generic orbits. For completeness, we reinstate the nonlocal terms relevant for elliptic-like motion up to 6PN/1SF in a small-eccentricity expansion. Via the connection between the (source) energy flux in [2210.05541] and tail effects, we also derive the SF-exact logarithmic-dependent part of the full 5PM bound Hamiltonian. Our results provide the most accurate description to date of the dynamics of bound compact objects within the framework of relativistic scattering computations.

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arXiv2025

Nonlinear Gravitational Radiation Reaction: Failed Tail, Memories & Squares

Using the Schwinger-Keldysh "in-in" effective field theory (EFT) framework, we complete the knowledge of nonlinear gravitational radiation-reaction effects in the (relative) dynamics of binary systems at fifth Post-Newtonian (5PN) order. Diffeomorphism invariance plays a key role guaranteeing that the Ward identities are obeyed (in background-field gauge). Nonlocal-in-time (memory) effects appear in the soft-frequency limit as boundary terms in the effective action, consistently with the loss of (canonical) angular momentum. We identify a conservative sector through Feynman's $i0^+$-prescription. Notably, terms at second order in the (linear) radiation-reaction force also produce conservative-like effects (as we likewise demonstrate in electromagnetism). For the sake of comparison, we derive the ${\cal O}(G^4)$ contribution to the total (even-in-velocity) 5PN relative scattering angle. We find perfect agreement in the overlap with the state of the art in the Post-Minkowskian expansion, both in the conservative and dissipative sectors, resolving the (apparent) discrepancy with previous EFT results. We will return to the full conservative part of the 5PN dynamics elsewhere.

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arXiv2024

Signatures of ultralight bosons in the orbital eccentricity of binary black holes

We show that the existence of clouds of ultralight particles surrounding black holes during their cosmological history as members of a binary system can leave a measurable imprint on the distribution of masses and orbital eccentricities observable with future gravitational-wave detectors. Notably, we find that for nonprecessing binaries with chirp masses ${\cal M} \lesssim 10\,M_\odot$, formed exclusively in isolation, larger-than-expected values of the eccentricity, i.e. $e\gtrsim 10^{-2}$ at gravitational-wave frequencies $f_{\rm GW} \simeq 10^{-2}\,$Hz, would provide tantalizing evidence for a new particle of mass between $[0.5,2.5] \times 10^{-12}\,$eV in nature. The predicted evolution of the eccentricity can also drastically affect the in-band phase evolution and peak frequency. These results constitute unique signatures of boson clouds of ultralight particles in the dynamics of binary black holes, which will be readily accessible with the Laser Interferometer Space Antenna, as well as future mid-band and Deci-hertz detectors.

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arXiv2024

Gravitational radiation from inspiralling compact binaries to N$^3$LO in the Effective Field Theory approach

Within the context of the Effective Field Theory (EFT) framework to gravitational dynamics, we compute the Hamiltonian, source quadrupole moment, and gravitational-wave energy flux for (non-spinning) inspiralling compact binaries at next-to-next-to-next-to leading order (N$^3$LO) in the Post-Newtonian (PN) expansion. We use the recently developed $d$-dimensional multipole-expanded effective theory, and explicitly perform the matching to the (pseudo-) stress-energy tensor. The calculation involves Feynman integrals up to three- (conservative) and two-loop (radiative) orders, evaluated within dimensional regularization. Our (ambiguity-free) results confirm (for the first time) the value of the gravitational-wave flux for quasi-circular orbits at 3PN order, while paving the way forward to the inclusion of spin effects as well as higher order computations.

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arXiv2024

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 (non-spinning) local-in-time conservative dynamics at fourth Post-Minkowskian order, i.e. ${\cal O}(G^4)$. This is achieved by computing the nonlocal-in-time contribution to the deflection angle, and removing it from the full conservative value in [2112.11296,2210.05541]. 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 elliptic-like 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 modelling.

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arXiv2023

Bootstrapping the relativistic two-body problem

We describe the formalism to compute gravitational-wave observables for compact binaries via the effective field theory framework in combination with modern tools from collider physics. We put particular emphasis on solving the "multi-loop" integration problem via the methodology of differential equations and expansion by regions. This allows us to "bootstrap" the two-body relativistic dynamics in the Post-Minkowskian (PM) expansion from boundary data evaluated in the near-static (soft) limit. We illustrate the procedure with the derivation of the total spacetime impulse in the scattering of non-spinning bodies to 4PM (three-loop) order, i.e. ${\cal O}(G^4)$, including conservative and dissipative effects.

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arXiv2022

Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order

We obtain the total impulse in the scattering of non-spinning binaries in general relativity at fourth Post-Minkowskian order, i.e. ${\cal O}(G^4)$, including linear, nonlinear, and hereditary radiation-reaction effects. We derive the total radiated spacetime momentum as well as the associated energy flux. The latter can be used to compute gravitational-wave observables for generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline effective field theory framework in combination with modern "multi-loop" integration techniques from collider physics. The complete results are in agreement with various partial calculations in the Post-Newtonian/Minkowskian expansion.

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arXiv2022

Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics

We extend the Post-Minkowskian (PM) effective field theory (EFT) approach to incorporate conservative and dissipative radiation-reaction effects in a unified framework. This is achieved by implementing the Schwinger-Keldysh "in-in" formalism and separating conservative and non-conservative terms according to the formulation in [1210.2745], which we show promotes Feynman's $i0$-prescription and cutting rules to a prominent role at the classical level. The resulting integrals, involving both Feynman and retarded propagators, can be bootstrapped to all orders in the velocity via differential equations with boundary conditions including potential and radiation modes. As a paradigmatic example we provide an ab initio derivation of the classical solution to the scattering problem in general relativity to ${\cal O}(G^3)$. For the sake of completeness, we also reproduce the leading order radiation-reaction effects in classical electrodynamics.

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arXiv2022

From Boundary Data to Bound States III: Radiative Effects

We extend the "boundary-to-bound" (B2B) correspondence to incorporate radiative as well as conservative radiation-reaction effects. We start by deriving a map between the total change in observables due to gravitational wave emission during hyperbolic-like motion and in one period of an elliptic-like orbit, which is valid in the adiabatic expansion for non-spinning as well as aligned-spin configurations. We also discuss the inverse problem of extracting the associated fluxes from scattering data. Afterwards we demonstrate, to all orders in the Post-Minkowskian expansion, the link between the radiated energy and the ultraviolet pole in the radial action in dimensional regularization due to tail effects. This implies, as expected, that the B2B correspondence for the conservative sector remains unchanged for local-in-time radiation-reaction tail effects with generic orbits. As a side product, this allows us to read off the energy flux from the associated pole in the tail Hamiltonian. We show that the B2B map also holds for non-local-in-time terms, but only in the large-eccentricity limit. Remarkably, we find that all of the trademark logarithmic contributions to the radial action map unscathed between generic unbound and bound motion. However, unlike logarithms, other terms due to non-local effects do not transition smoothly to quasi-circular orbits. We conclude with a discussion on these non-local pieces. Several checks of the B2B dictionary are displayed using state-of-the-art knowledge in Post-Newtonian/Minkowskian theory.

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arXiv2022

Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics

Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to ${\cal O}(G^2)$, which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

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arXiv2022

Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach

We present the contribution from potential interactions to the dynamics of non-spinning binaries to fourth Post-Minkowskian (4PM) order. This is achieved by computing the scattering angle to ${\cal O}(G^4)$ using the effective field theory approach and deriving the bound radial action through analytic continuation. We reconstruct the Hamiltonian and center-of-mass momentum in an isotropic gauge. The (three-loop) integrals involved in our calculation are computed via differential equations, including a sector yielding elliptic integrals. Using the universal link between potential and tail terms, we also report: 1) The instantaneous energy flux at ${\cal O}(G^3)$; 2) The contribution to the 4PM unbound/bound radial action(s) depending on logarithms of the binding energy; 3) The (scheme-independent) logarithmic contribution to the 4PM non-local tail Hamiltonian for circular orbits. Our results in the potential region are in agreement with the recent derivation from scattering amplitudes. We also find perfect agreement in the overlap with the state-of-the-art in Post-Newtonian theory.

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arXiv2022

Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion

We compute the conservative dynamics of non-spinning binaries at fourth Post-Minkowskian order in the large-eccentricity limit, including both potential and radiation-reaction tail effects. This is achieved by obtaining the scattering angle in the worldline effective field theory approach and deriving the bound radial action via analytic continuation. The associated integrals are bootstrapped to all orders in velocities through differential equations, with boundary conditions in the potential and radiation regions. The large angular momentum expansion captures all the local-in-time effects as well as the trademark logarithmic corrections for generic bound orbits. Agreement is found in the overlap with the state-of-the-art in Post-Newtonian theory.

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arXiv2022

Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order

The linear- and quadratic-in-spin contributions to the binding potential and gravitational-wave flux from binary systems are derived to next-to-next-to-leading order in the Post-Newtonian (PN) expansion of general relativity, including finite-size and tail effects. The calculation is carried out through the worldline effective field theory framework. We find agreement in the overlap with the available PN literature and test-body limit. As a direct application, we complete the knowledge of spin effects in the evolution of the orbital phase for aligned-spin circular orbits to fourth PN order. We estimate the impact of the new results in the number of accumulated gravitational-wave cycles. We find they will play an important role in providing reliable physical interpretation of gravitational-wave signals from spinning binaries with future detectors such as LISA and the Einstein Telescope.

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arXiv2021

Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order

Using the gravitational potential and source multipole moments bilinear in the spins, first computed to next-to-leading order (NLO) in the post-Newtonian (PN) expansion within the effective field theory (EFT) framework, we complete here the derivation of the dynamical invariants and flux-balance equations, including energy and angular momentum. We use these results to calculate spin-spin effects in the orbital frequency and accumulated phase to NLO for circular orbits. We also derive the linear momentum and center-of-mass fluxes and associated kick-velocity, to the highest relevant PN order. We explicitly demonstrate the equivalence between the quadratic-in-spin source multipoles obtained using the EFT formalism and those rederived later with more traditional tools, leading to perfect agreement for spin-spin radiative observables to NLO among both approaches.

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arXiv2020

Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach

We derive the conservative dynamics of non-spinning binaries to third Post-Minkowskian order, using the Effective Field Theory (EFT) approach introduced in [2006.01184] together with the Boundary-to-Bound dictionary developed in [1910.03008, 1911.09130]. The main ingredient is the scattering angle, which we compute to ${\cal O}(G^3)$ via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated (master) integrals are bootstrapped to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same integrals that appear in the EFT with Post-Newtonian sources. For the sake of comparison, we reconstruct the Hamiltonian and the classical limit of the scattering amplitude. Our results are in perfect agreement with those in Bern et al. [1901.04424, 1908.01493].

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