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Bound-Unbound Universality and the All-Order Semi-Classical Wave Function in Schwarzschild

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arxiv 2503.23317 v2 pith:TNRRDAEQ submitted 2025-03-30 gr-qc hep-th

Majed Khalaf , Chia-Hsien Shen , Ofri Telem This is my paper
classification gr-qchep-th
keywords methodrelativisticschwarzschildbound-unboundmotiontime-dependentcoulombexpressions
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abstract

We present a systematic method for analytically computing time-dependent observables for a relativistic probe particle in Coulomb and Schwarzschild backgrounds. The method generates expressions valid both in the bound and unbound regimes, namely bound-unbound universal expressions. To demonstrate our method we compute the time-dependent radius and azimuthal angle for relativistic motion in a Coulomb background (relativistic Keplerian motion), as well as the electromagnetic field radiated by a relativistic Keplerian source. All of our calculations exhibit bound-unbound universality. Finally, we present an exact expression for the semi-classical wave function in Schwarzschild. The latter is crucial in applying our method to any time-dependent observable for probe-limit motion in Schwarzschild, to any desired order in velocity and the gravitational constant $G$.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Analytical Fluxes from Generic Schwarzschild Geodesics

    gr-qc 2026-05 unverdicted novelty 7.0 of 10

    An analytic Chebyshev-expansion method computes gravitational-wave fluxes from arbitrary-eccentricity Schwarzschild geodesics by reducing them to sums of prior Keplerian Fourier coefficients, with numerical tests show...

  2. Resumming Scattering Amplitudes for Waveforms

    hep-th 2026-01 unverdicted novelty 7.0 of 10

    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.

  3. Analytical Fluxes from Generic Schwarzschild Geodesics

    gr-qc 2026-05 conditional novelty 6.0 of 10

    A Chebyshev-basis expansion reduces gravitational-wave fluxes from arbitrary-eccentricity bound Schwarzschild geodesics to sums of previously derived Keplerian Fourier coefficients, achieving 10^{-5} relative accuracy...

  4. Resummed energy loss in extreme-mass-ratio scattering using critical orbits

    gr-qc 2026-02 conditional novelty 6.0 of 10

    Near-separatrix logarithmic divergence, anchored by fitted unstable-circular-orbit fluxes, yields resummed formulas for energy loss in extreme-mass-ratio scattering that track exact numerical calculations to about 10-25%.

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