Exact tree-level MHV graviton scattering amplitudes at arbitrary multiplicity are obtained on self-dual Taub-NUT backgrounds using twistor theory, including spin via Newman-Janis shift, with undeformed celestial symmetries.
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Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
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abstract
We demonstrate equivalences, under simple mappings, between the dynamics of three distinct systems---(i) an arbitrary-mass-ratio two-spinning-black-hole system, (ii) a spinning test black hole in a background Kerr spacetime, and (iii) geodesic motion in Kerr---when each is considered in the first post-Minkowskian (1PM) approximation to general relativity, i.e. to linear order $G$ but to all orders in $1/c$, and to all orders in the black holes' spins, with all orders in the multipole expansions of their linearized gravitational fields. This is accomplished via computations of the net results of weak gravitational scattering encounters between two spinning black holes, namely the net $O(G)$ changes in the holes' momenta and spins as functions of the incoming state. The results are given in remarkably simple closed forms, found by solving effective Mathisson-Papapetrou-Dixon-type equations of motion for a spinning black hole in conjunction with the linearized Einstein equation, with appropriate matching to the Kerr solution. The scattering results fully encode the gauge-invariant content of a canonical Hamiltonian governing binary-black-hole dynamics at 1PM order, for generic (unbound and bound) orbits and spin orientations. We deduce one such Hamiltonian, which reproduces and resums the 1PM parts of all such previous post-Newtonian results, and which directly manifests the equivalences with the test-body limits via simple effective-one-body mappings.
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UNVERDICTED 9representative citing papers
Generalized Carter and Rüdiger constants for spinning charged probes in √Kerr backgrounds exist only for Wilson coefficients matching spin-exponentiated effective Compton amplitudes up to second order in spin.
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.
Four relativistic spinning particle models (vector oscillator, spinor oscillator, spherical top, massive twistor) describe identical physics in free and interacting theories within the spin-magnitude-preserving sector.
A BRST formulation yields a single constraint per off-shell quartic vertex ensuring gauge invariance and associativity, with example solutions for low-spin cases in black hole scattering.
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.
In five dimensions, minimally coupled massive vector and antisymmetric tensor fields produce only mass or stress quadrupoles respectively from scattering amplitudes, failing to match the Myers-Perry black hole and demonstrating breakdown of spin universality.
In the root-Kerr probe model, integrability holds to all spin orders at leading probe charge under Newman-Janis vertices but fails at spin-cubic order at second charge order and cannot be restored by further action deformation.
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.
citing papers explorer
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Graviton scattering on self-dual black holes
Exact tree-level MHV graviton scattering amplitudes at arbitrary multiplicity are obtained on self-dual Taub-NUT backgrounds using twistor theory, including spin via Newman-Janis shift, with undeformed celestial symmetries.
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Generalized Carter & R\"udiger Constants of $\sqrt{\text{Kerr}}$
Generalized Carter and Rüdiger constants for spinning charged probes in √Kerr backgrounds exist only for Wilson coefficients matching spin-exponentiated effective Compton amplitudes up to second order in spin.
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The Classical Gravitational Impulse at High Energies
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.
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Universality in Relativistic Spinning Particle Models
Four relativistic spinning particle models (vector oscillator, spinor oscillator, spherical top, massive twistor) describe identical physics in free and interacting theories within the spin-magnitude-preserving sector.
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BRST methods for constructing quartic actions for spinning black holes
A BRST formulation yields a single constraint per off-shell quartic vertex ensuring gauge invariance and associativity, with example solutions for low-spin cases in black hole scattering.
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Unexpected Symmetries of Kerr Black Hole Scattering
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.
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Gravitational multipoles from scattering amplitudes in higher dimensions
In five dimensions, minimally coupled massive vector and antisymmetric tensor fields produce only mass or stress quadrupoles respectively from scattering amplitudes, failing to match the Myers-Perry black hole and demonstrating breakdown of spin universality.
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On the integrability of root-Kerr probe dynamics
In the root-Kerr probe model, integrability holds to all spin orders at leading probe charge under Newman-Janis vertices but fails at spin-cubic order at second charge order and cannot be restored by further action deformation.
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All-order structure of static gravitational interactions and the seventh post-Newtonian potential
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.