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The Radial Action from Probe Amplitudes to All Orders
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We extract the relativistic classical radial action from scattering amplitudes, to all orders in perturbation theory, in the probe limit. Our sources include point charges and monopoles, as well as the Schwarzschild and pure-NUT gravitational backgrounds. A characteristic relativistic effect, that scattering trajectories may wind around these sources any number of times, can be recovered when all-order amplitudes are available. We show that the amplitude for scattering a probe off a pure NUT is given by the solution of a transcendental equation involving continued fractions, and explain how to solve this equation to any desired loop order.
Forward citations
Cited by 2 Pith papers
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Memory effect from the scattering of Taub-NUT black holes
Soft theorems yield a gauge-invariant nutty soft factor and the associated memory tensor for Kerr-Taub-NUT scattering, with magnetic components and directional divergences absent in electromagnetism.
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Topological Stars and scalar wave equation: Exact resummation of the renormalized angular momentum in the eikonal limit
For Topological Stars, the eikonal-limit renormalized angular momentum is expressed as hypergeometric functions tied to the null geodesic radial action, generalizing the Schwarzschild resummation.
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