Nonlocal-in-time conservative tail contributions to gravitational scattering are derived at 5PM and 10SF orders, expressed via polylogarithms up to weight three and agreeing with prior results through 6PN.
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Emergence of Calabi-Yau manifolds in high-precision black hole scattering
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Using the worldline quantum field theory formalism, we compute the radiation-reacted impulse, scattering angle, radiated energy and recoil of a classical black hole (or neutron star) scattering event at fifth post-Minkowskian and sub-leading self-force orders (5PM-1SF). This state-of-the-art four-loop computation employs advanced integration-by-parts and differential equation technology, and is considerably more challenging than the conservative 5PM-1SF counterpart. As compared with the conservative 5PM-1SF, in the radiation sector Calabi-Yau three-fold periods appear and contribute to the radiated energy and recoil observables. We give an extensive exposition of the canonicalization of the differential equations and provide details on boundary integrations, Feynman rules, and integration-by-parts strategies. Comparisons to numerical relativity are also performed.
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UNVERDICTED 22representative citing papers
Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in the Gauss-Manin connection.
Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
A new projector-based formalism determines effective potentials from perturbative amplitudes and resums them to compute non-perturbative gravitational waveforms for generic two-body trajectories.
Computes the leading double logarithm at 5PM in the high-energy gravitational amplitude via multi-H diagrams and dispersion relations, extracting the single-log imaginary part of the eikonal phase.
Authors define Kerr generating functions for all-loop scattering on Kerr black holes and apply them to compute leading non-linear tidal effects of neutron stars up to four loops in gravity.
The gravitational impulse for ultrarelativistic massive scalars is resummed to all orders in G_N at fixed G_N s/mb, recovering post-Minkowski results and predicting the leading high-energy behavior to eleventh post-Minkowski order.
The authors introduce static correlators in worldline QFT to compute angular momentum dissipation in black hole scattering, reproducing the known O(G^3) flux and extending the approach to electromagnetism at O(α^3).
Black hole response theory in WQFT exactly reproduces the Aichelburg-Sexl shockwave metric, geodesics, and the transfer matrix for gravitational-wave scattering off it via post-Minkowskian resummation.
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
Derives 5PN scattering observables and a conservative Hamiltonian contribution for black holes that determines EOB parameters d5loc and a6loc.
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.
Derives conservative potential and scattering angle for charged black holes in EMD theory via one-loop soft amplitudes, showing IR finiteness after Lippmann-Schwinger treatment and smooth reduction to GR.
The work establishes conservation of several quantities in Kerr black hole scattering and presents evidence that a spinning probe satisfies asymptotic integrability to quartic spin order at all post-Minkowskian orders.
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
A Legendre transform establishes an exact duality between the classical Polchinski equation and the authors' classical RG equation for the gravitational effective action.
Embedding classical Hamilton-Jacobi amplitude and phase into a complex field yields a linear equation from which quantum mechanics emerges structurally when the real part of a scaling parameter is nonzero.
Self-force calculations of radiated gravitational wave energy from hyperbolic orbits around Schwarzschild black holes agree with post-Minkowskian results for large impact parameters and velocities up to 0.7c, with further comparisons to post-Newtonian and numerical relativity.
The paper provides state-of-the-art predictions for the Einstein Telescope's impact on fundamental physics, cosmology, compact-object astrophysics, and multi-messenger astronomy across its proposed configurations.
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Black Hole Dynamics at Fifth Post-Newtonian Order
Derives 5PN scattering observables and a conservative Hamiltonian contribution for black holes that determines EOB parameters d5loc and a6loc.